Dear all,
One can use a mixed-model framework to estimate repeatability (R) of a trait, for example a behavioral trait. Repeatability is calculated based on the two variance components obtained from the model: residual (within-individual variance) and random (between-individual variance). The good point about using mixed-models for estimating R is that one can account for confounding (fixed or random) effects, and model correlation and heteroscedasticity, among other advantages.
A key reference in the topic explains that: "Data-level predictors that are associated with individual data points will usually increase the repeatability estimates (such as age if the same individual was measured at different ages), since they tend to reduce residual variance . On the contrary, individual-level predictors that vary between individuals (such as hatching order or sex) will usually decrease both agreement and adjusted repeatability, since they reduce the between-group variance (Gelman & Hill, 2007). Confounding factors that vary within as well as between individuals may decrease or increase both types of repeatability depending on the nature of the trade-offs" Nakagawa and Schielzeth, 2010.
When working on a mixed-model approach, however, sometimes it can be necessary to account for correlation of the residuals (for example for traits repeatedly measured over time) using correlation structures like corAR1 in lme. Similarly, one might need to account for heteroscedasticity incorporating a weights argument to the model (in the case of lme in R).
When this is neccessary, what is the predicted effects of those terms on the random and residual variances (and therefore in R): increase, decrease or unpredictable?
Thank you so much.
David
Hi David,
These are two operate independently because they address separate issues. Adjusting standard errors (ie., robust) to account for heterogeneity impacts the fixed effects portion of your model. The covariance type is for the random effects portion of your model.
So if you use robust std errors, you will increase the standard error and thus the confidence intervals, making the fixed effects more conservative (harder to prove statistical significance).
The covariance types for the random effects are as follows (at least in Stata):
independent - one variance parameter per random effect, all covariances zero; the default unless a factor variable is specified
exchangeable - equal variances for random effects, and one common pairwise covariance
identity - equal variances for random effects, all covariances zero; the default for factor variables
unstructured - all variances and covariances distinctly estimated
I hope this helps
Ariel
Dear Ariel.
Thank you for your response.
Actually, I understand that heteroscedasticity and correlation structure act on different parts of the model. So:
1- If I model heteroscedasticity I make the fixed effects more conservative, but what is the effect on the residual variance of the model, as compared to a model in which heteroscedasticity is not accounted for? Increase or decrease? I guess there is no effect on the random variance, right?
2- The covariance structures you propose are used in multivariate models, right? And you want to specifiy how these variable covary... However, my question referred to a univariate model with a single random intercept. Including a corAR1 (for instance) in lme(), how wil impact the random variance (as compared to a model without corAR1)? Increase or decrease? Is there any predicted effect on the residual variance?
I´m very interested in those variances because they define the repeatability of the trait which is being analysed.
Thanks and greetings.
David
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