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Instructions
The salamander dataset (salamander.csv) contains information from McCullagh and Nelder (1989).
Three tests on salamander mating were carried out: two in the autumn and one in the summer of the same year, using different salamanders. The response variable is binary, indicating whether or not the mating was successful. In each experiment, 20 females and 20 males from two locations termed whiteside (W) and rough butt (R) were matched six times for mating with individuals from their own and the other location, for a total of 120 observations.
It has the following variables:
Mating: Have the salamanders mated? (1=yes)
Cross: Denotes a sex/population split. The first letter indicates the female’s population, whereas the second letter indicates the male’s population.
Male: A unique identification for males.
Female: A unique identity for females.
The command can be used to load and format data.
read.csv – salamander (“salamander.csv”)
salamander$Male – as.factor(salamander$Male) salamander$Female – as.factor(salamander$Female) salamander$Male – as.factor(salamander$Male)
a. For each cross, calculate the proportion of successful mating attempts. Are there any patterns that you’ve noticed?
b. Fit the data to a generalized linear model, utilizing the cross category to predict mating success without using random effects. Are there any significant differences between levels in the fixed effect estimates?
b. Using the numerical integration approach, fit a GLMM to the data. The individual Male and Female salamanders should be treated as random effects in this model, and mating success should be related to the cross of the pairing. Report the fixed effect coefficient values once more.
d. Compare the coefficient estimates from parts b and c of the models. Are the fixed effects in the GLM and GLMM very different? Remember to think in terms of the estimations’ standard errors.
d. (7510 only) Model mating success as a function of cross using a Bayesian GLMM with both the Male and Female IDs as random effects. For the distribution, use family=categorical.
To get a stable fit, you’ll need to experiment with the amount of iterations, burnin, and priors.
Report the coefficient estimates and compare them to the prior models whenever you’re pleased. Always doublecheck diagnostics.
1
2) The BodyWeight dataset in the nlme package comprises information on rats’ body weights over a period of 64 days. On day 1, the rats’ body weights (in grams) are measured, and then every seven days until day 64, with an additional measurement on day 44. Several weeks prior to “day 1,” the experiment began. Three groups of rats, each on a different diet, are present.
It has the following variables:
weight: the rat’s body weight in grams.
Time: The number of days at which the measurement is taken.
Rat: This is the rat whose weight is being measured.
Diet: A factor with numbers ranging from 1 to 3 that indicates the rat’s diet.
The command can be used to load and format data.
data(BodyWeight,package = “nlme”) data(BodyWeight,package = “nlme”) data(BodyWeight,
a. Plot the data as weight vs. time with ratspecific lines to highlight the subjectspecific trajectory.
Describe what you discovered. (Only 7510) Additionally, for each diet, color the lines differently. Is there anything else you’ve noticed?
b. Fit a linear regression model that describes how weight varies with days to each individual rat using the lmList function. What are the differences between slopes and intercepts? Are there any diet patterns that you’ve noticed?
c. Create a mixed effects model that depicts how the rats’ weight changes linearly over time while accounting for random variation in their intercepts. Examine the interept’s fixed effect estimate and remark on its significance in the context of the rat’s variance component.
c. Get the BLUPs for the rats and make a list of who is the heaviest.
e. Create a mixed effects model that captures how the rats’ weight changes linearly over time while accounting for random variation in intercepts and slopes. Calculate the random effect confidence intervals; do the slopes and intercepts appear to differ between subjects? This model’s convergence may be a concern. To use a different optimizer, use the control=lmerControl(optimizer=Nelder Mead) option in lmer().
f. Collect BLUPs for the model in part a. Which rat’s growth rate is the fastest? Who’s the slowest?
Using the fixed effect estimate for time and their BLUP value, calculate the values of their particular slopes. Print the data for these two rats and make a note of their lowest and highest weights during the duration of the experiment.
g. Include the diet variable in the model as a timedependent interaction. Is there a connection between nutrition and weight?
Is there a difference in the effect at different times?
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STAT 4520/7520 Questions on Applied Statistics 