Conditional Logistic Regression With Longitudinal Follow-up and Individual-Level Random Coefficients: A Stable and Efficient Two-Step Estimation Method

Abstract

The analysis of data generated by animal habitat selection studies, by family studies of genetic diseases, or by longitudinal follow-up of households often involves fitting a mixed conditional logistic regression model to longitudinal data composed of clusters of matched case-control strata. The estimation of model parameters by maximum likelihood is especially difficult when the number of cases per stratum is greater than one. In this case, the denominator of each cluster contribution to the conditional likelihood involves a complex integral in high dimension, which leads to convergence problems in the numerical maximization. In this article we show how these computational complexities can be bypassed using a global two-step analysis for nonlinear mixed effects models. The first step estimates the cluster-specific parameters and can be achieved with standard statistical methods and software based on maximum likelihood for independent data. The second step uses the EM-algorithm in conjunction with conditional restricted maximum likelihood to estimate the population parameters. We use simulations to demonstrate that the method works well when the analysis is based on a large number of strata per cluster, as in many ecological studies. We apply the proposed twostep approach to evaluate habitat selection by pairs of bison roaming freely in their natural environment. This article has supplementary material online.

Oceanographic drivers of winter habitat use in Cassin’s Auklets

“…Unlike commonly used GAMs and GLMMs, SSFs estimate more robust and interpretable coefficients when modeling resource selection, relating movement to environmental covariates by accounting for spatial and temporal constraints of the movement process (Craiu et al. ). Step‐selection functions have become more prevalent in movement studies of terrestrial vertebrates (Thurfjell et al.…”

“…This involved applying the Ts.estim() function in the package TwoStepCLogit to first estimate coefficients for each individual and then combining those estimates using restricted maximum likelihood to achieve population‐level coefficients (Craiu et al. ). This provided a pragmatic, robust method for dealing with individual variation when estimating selection parameters (Murtaugh ).…”

Robust Inference from Conditional Logistic Regression Applied to Movement and Habitat Selection Analysis

“…They do illustrate, however, how the difference between the marginal effects and the conditional effects (values of , used in the simulations) increases as the heterogeneity or autocorrelation increase (see detailed discussion of this phenomenon in Craiu et al [19] and Fieberg et al [17]).…”

“…If applied when there is no temporal autocorrelation or when individuals have largely distinct behaviours, the robust estimate of variance remains biased, and conclusions regarding resource selection behaviour may be unreliable. Thus, an assessment of the presence of temporal autocorrelation (using an autocorrelation function for example, see [25]) and inter-individual heterogeneity (using individual-level random coefficients, see [19]) should be performed before using destructive sampling.…”

“…It has become common practice to use generalized estimating equations (GEE) to cope with temporal autocorrelation in longitudinal data [9,10,17,18]. GEE have also to account for a second source of non-independence in successive observations [3,19]. Indeed, individuals may react differently to various habitat features due to differences in their experience, social status, age, sex, and physical condition [18,20–22].…”