2023 Homework, week 4

This homework covers the material from Lectures 7 and 8, and the content from book Chapters 7, 8, and 9. The questions are reproduced almost identically from Richard McElreath’s original assignment, I did not write them. I only wrote these solutions.

library(rethinking)

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- CmdStanR documentation and vignettes: mc-stan.org/cmdstanr

- CmdStan path: C:/Users/Zane/.cmdstan/cmdstan-2.34.1

- CmdStan version: 2.34.1

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rethinking (Version 2.40)

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1. Revisit the marriage, age, and happiness collider bias example from Chapter 6. Run models m6.9 and m6.10 again (pages 178-179). Compare these two models using both PSIS and WAIC. Which model is expected to make better predictions, according to these criteria, and which model yields the correct causal inference?

OK, first we will fit the models. Since these are exactly the same as in the book, the results will be similar and I won’t spend a lot of time on them.

# Data setup
d <- sim_happiness(seed = 1977, N_years = 1000)
d2 <- d[d$age > 17, ]
d2$A <- (d2$age - 18) / (65 - 18)
d2$M <- d2$married + 1

set.seed(134123)

# First model: 
m6.9 <-
    quap(
        alist(
            happiness ~ dnorm(mu, sigma),
            mu <- a[M] + bA * A,
            a[M] ~ dnorm(0, 1),
            bA ~ dnorm(0, 2),
            sigma ~ dexp(1)
        ),
        data = d2
    )

# Second model
m6.10 <-
    quap(
        alist(
            happiness ~ dnorm(mu, sigma),
            mu <- a + bA * A,
            a ~ dnorm(0, 1),
            bA ~ dnorm(0, 2),
            sigma ~ dexp(1)
        ),
        data = d2
    )

OK, now we want to score the models by PSIS and WAIC. Let’s do PSIS first.

PSIS(m6.9)

      PSIS      lppd  penalty  std_err
1 2713.834 -1356.917 3.687653 37.43357

PSIS(m6.10)

      PSIS      lppd  penalty  std_err
1 3101.878 -1550.939 2.321511 27.82064

And now the WAIC.

WAIC(m6.9)

      WAIC      lppd  penalty  std_err
1 2713.726 -1353.256 3.606974 37.38137

WAIC(m6.10)

     WAIC      lppd penalty  std_err
1 3102.34 -1548.622 2.54812 27.77344

OK, so for this model they are basically the same. But either way, we see that model m6.9, which stratifies by marriage, is better at prediction! However, we know that m6.10 actually makes the correct causal inference. This should not surprised us, because colliders contain information – even if they distort causal estimates, including them will often work better for prediction.

2. Reconsider the urban fox analysis from last week’s homework. On the basis of PSIS and WAIC scores, which combination of variables best predicts body weight? What causal interpretation can you assign each coefficient from the best scoring model?

First I’ll fit the two models that we were using at the end of last week’s homework – the model for the direct effect of \(F\) and the model for the total effect of \(F\) (which we recall that we could not accurately estimate due to an unmeasured confounder). We’ll also add an additional “kitchen sink” model that includes age (even though it is a precision parasite), just because we also have that. There are seven different models that we could choose, but I think these three will probably be sufficient.

# Set up data
data(foxes)
D <-
    foxes |>
    dplyr::select(
        F = avgfood,
        A = area,
        W = weight,
        G = groupsize
    ) |>
    dplyr::mutate(
        dplyr::across(dplyr::everything(), standardize)
    ) |>
    as.list()

# Fit the two models
set.seed(193482)
kitchen_sink <-
    rethinking::quap(
        flist = alist(
            W ~ dnorm(mu, sigma),
            mu <- a + bF * F + bG * G + bA * A,
            a ~ dnorm(0, 2),
            bF ~ dnorm(0, 2),
            bG ~ dnorm(0, 2),
            bA ~ dnorm(0, 2),
            sigma ~ dexp(1)
        ),
        data = D,
        control = list(maxit = 500)
    )
f_direct <-
    rethinking::quap(
        flist = alist(
            W ~ dnorm(mu, sigma),
            mu <- a + bF * F + bG * G,
            a ~ dnorm(0, 2),
            bF ~ dnorm(0, 2),
            bG ~ dnorm(0, 2),
            sigma ~ dexp(1)
        ),
        data = D,
        control = list(maxit = 500)
    )
f_total <-
    rethinking::quap(
        flist = alist(
            W ~ dnorm(mu, sigma),
            mu <- a + bF * F,
            a ~ dnorm(0, 2),
            bF ~ dnorm(0, 2),
            sigma ~ dexp(1)
        ),
        data = D,
        control = list(maxit = 500)
    )

coeftab(kitchen_sink, f_direct, f_total) |>
    coeftab_plot(pars = c("bA", "bF", "bG"))

OK, now we can calculate the PSIS and WAIC for all of these.

sapply(list(kitchen_sink, f_direct, f_total), PSIS) |>
    `colnames<-`(c("A, G, F", "F, G", "F"))

        A, G, F   F, G      F        
PSIS    324.0635  324.3235  333.7011 
lppd    -162.0317 -162.1617 -166.8506
penalty 5.523674  4.297541  2.555102 
std_err 17.02429  16.84845  13.91888 

sapply(list(kitchen_sink, f_direct, f_total), WAIC) |>
    `colnames<-`(c("A, G, F", "F, G", "F"))

        A, G, F   F, G      F       
WAIC    323.9801  324.5721  334.1936
lppd    -156.4935 -157.8467 -164.32 
penalty 5.496565  4.43933   2.776743
std_err 16.89324  17.05316  13.91089

Here we get a little bit of a competition, but not much of one. We can see that the “kitchen sink” model wins by less than a point for PSIS, but the direct causal model wins by less than a point for WAIC. That’s obviously due to approximation error, it doesn’t matter which one wins by just a few points. Clearly we can see that the model for the direct causal effect beats out the model for the total causal effect, which makes sense because both of these variables encode unique information about the outcome (from our causal model, \(A\) does not).

For the best model, we can infer the direct causal effects of \(F\) and \(G\), but not the total causal effect of \(F\).

3. Build a predictive model of the relationship shown on the cover of the book, the relationship between the timing of cherry blossoms and March temperature in the same year. The data are found in data(cherry_blossoms). Consider at least two different models (functional relationships) to predict doy with temp. Compare them with PSIS or WAIC.

Suppose March temperatures reach 9 degrees by the year 2050. What does your best model predict for the predictive distribution of the day-in-year that the cherry trees will blossom?

OK, I feel like I kind of already did this one in the textbook work I’ve done, but let’s go through it as a fun exercise anyways. First we need to process the data, which I’ll do the same way he did in the book.

data("cherry_blossoms")
d <- cherry_blossoms
d2 <- d[complete.cases(d$doy, d$temp), ]

# Also standardize the data
d3 <-
    list(
        doy = standardize(d2$doy),
        temp = standardize(d2$temp)
    )

I’ll compare the null model, a linear model, a quadratic model, and a spline-based model similar to the one from the book. I’ll just use kind of random priors on this without a lot of explanation, just fiddling until the models seems to work correctly. Then I’ll compare the models.

# Null model (intercept only)
q3_m1 <-
    quap(
        alist(
            doy ~ dnorm(mu, sigma),
            mu <- a,
            a ~ dnorm(0, 3),
            sigma ~ dexp(1)
        ),
        data = d3
    )

# Linear model
q3_m2 <-
    quap(
        alist(
            doy ~ dnorm(mu, sigma),
            mu <- a + b * temp,
            a ~ dnorm(0, 3),
            b ~ dnorm(0, 3),
            sigma ~ dexp(1)
        ),
        data = d3
    )

# Quadratic model
q3_m3 <-
    quap(
        alist(
            doy ~ dnorm(mu, sigma),
            mu <- a + b1 * temp + b2 * (temp ^ 2),
            a ~ dnorm(0, 3),
            b1 ~ dnorm(0, 3),
            b2 ~ dnorm(0, 3),
            sigma ~ dexp(1)
        ),
        data = d3
    )

# Power law model
q3_m4 <-
    quap(
        alist(
            doy ~ dnorm(mu, sigma),
            mu <- a + b * temp,
            a ~ dnorm(0, 3),
            b ~ dnorm(0, 3),
            sigma ~ dexp(1)
        ),
        data = list(
            doy = standardize(log(d2$doy)),
            temp = standardize(log(d2$temp))
        )
    )

# Spline model
# Create the splits
nk <- 15
knot_list <- quantile(d3$temp, probs = seq(0, 1, length.out = nk))
B <-
    splines::bs(
        x = d3$temp,
        knots = knot_list[-c(1, nk)],
        degree = 3,
        intercept = TRUE
    )

q3_m5 <-
    quap(
        flist = alist(
            doy ~ dnorm(mu, sigma),
            mu <- a + B %*% w,
            a ~ dnorm(100, 10),
            w ~ dnorm(0, 10),
            sigma ~ dexp(1)
        ),
        data = list(doy = d3$doy, B = B),
        start = list(w = rep(0, ncol(B)))
    )

All the models fit fine so I assume my randomly guessed priors were OK. First we’ll compare with WAIC.

compare(q3_m1, q3_m2, q3_m3, q3_m4, q3_m5)

          WAIC       SE     dWAIC        dSE     pWAIC       weight
q3_m2 2149.026 40.95329  0.000000         NA  2.721421 6.209027e-01
q3_m3 2151.255 41.03282  2.228806  0.2597071  3.724725 2.037251e-01
q3_m4 2151.557 42.18830  2.531068  5.5127294  3.057807 1.751496e-01
q3_m5 2164.893 41.43704 15.866859  8.0200012 17.965816 2.226276e-04
q3_m1 2236.671 39.77412 87.644915 16.8970472  2.121330 5.769951e-20

And now with PSIS.

compare(
    q3_m1, q3_m2, q3_m3, q3_m4, q3_m5,
    sort = "PSIS",
    func = PSIS
)

Some Pareto k values are high (>0.5). Set pointwise=TRUE to inspect individual points.

          PSIS       SE     dPSIS        dSE     pPSIS       weight
q3_m2 2149.271 40.84579  0.000000         NA  2.841805 5.643948e-01
q3_m3 2150.928 41.03927  1.657495  0.2972671  3.559165 2.464124e-01
q3_m4 2151.458 42.14878  2.187364  5.5039158  3.004142 1.890615e-01
q3_m5 2166.003 41.54788 16.731654  8.1282313 18.531424 1.313259e-04
q3_m1 2236.743 39.70714 87.471828 16.8454321  2.157284 5.718959e-20

OK, so both the WAIC the the PSIS comparison give us the same result. The linear model is actually the best fit, jujst by a hair. If we take the SE into account, the linear, quadratic, and power law models all seem to fit pretty decent. The spline model is a bit worse, within one SE, and all of the “real” models are better than the null model. My guess is that while the spline model is flexible, it doesn’t gain enough predictive power from this flexibility in order to be “worth” the large number of parameters needed.

Now let’s plot the results to get a better idea of what we’re looking at.

post <- sim(q3_m2)
out <- colMeans(post * sd(d2$doy) + mean(d2$doy))
plot(
    d2$doy, out,
    xlab = "Actual DoY", ylab = "Predicted DoY"
)

plot(
    d2$year, d2$doy, type = "l"
)
shade(
    apply(post, 2, \(x) rethinking::PI(x* sd(d2$doy) + mean(d2$doy)) ),
    d2$year,
    col = rethinking::col.alpha("gray", alpha = 0.75)
)
lines(d2$year, out, col = "red", lwd = 3)

plot(
    NULL, xlim = range(d2$year), ylim = c(-20, 20)
)
shade(
    apply(post, 2, \(x) rethinking::PI(x  * sd(d2$doy) + mean(d2$doy) - d2$doy)),
    d2$year,
    col = rethinking::col.alpha("gray", alpha = 0.75)
)

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Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length
Warning in x * sd(d2$doy) + mean(d2$doy) - d2$doy: longer object length is not
a multiple of shorter object length

lines(d2$year, out - d2$doy, type = "l", col = "red", lwd = 2)

Finally, let’s look at the distribution of predictions for if we set the temperature to 9 degrees.

4. The data in data(Dinosaurs) are body mass estimates at different estimated ages for six different dinosaur species. Choose one or more of these species and make a predictive model of body mass using age as a predictor. Consider two or more model types for the function relating age to body mass and score each using PSIS and WAIC.

Which model do you think is best, on predictive grounds? On scientific grounds? If your answers to these questions differ, why?