The Social Relations Model for Count Data

Tom Loeys,Jenae M Neiderhiser,Justine Loncke,William L Cook

doi:10.1027/1614-2241/a000178

Tom Loeys, Jenae M Neiderhiser + Show 2 more

Open Access

https://doi.org/10.1027/1614-2241/a000178

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Abstract

Abstract. The social relations model (SRM) is typically used to identify sources of variance in interpersonal dispositions in families. Traditionally, it uses dyadic measurements that are obtained from a round-robin design, where each family member rates each other family member. Those dyadic measurements are mostly considered to be continuous, but we, however, will discuss how the SRM can be adapted to count dyadic measurements. Such SRM for count data can be formulated in the SEM-framework by viewing it as a confirmatory factor analysis (CFA), but it can also be defined in the multilevel framework. These two frameworks result in equivalent models of which the parameters can be estimated using maximum likelihood estimation or a Bayesian approach. We perform a simulation study to compare the performance of those two estimators. As an illustration, we consider intergenerational co-activity data from a block design and contrast family dynamics between non-divorced families and stepfamilies.

Highlights

The main challenge that we will tackle in this paper lies in the nature of the dyadic measurements obtained from a block or round robin design
The Bayesian estimator can only be derived using the multilevel framework. Such Bayesian approach has already been proposed for the social relations model (SRM) without family roles, where the continuous outcomes are obtained according to a round robin design (Lüdtke, Robitzsch, Kenny, & Trautwein, 2012) and for categorical dyadic measurements (Hoff, 2015), such as count measurements (Koster & Leckie, 2014; Koster, Leckie, Miller, & Hames, 2015)
Since the family SRM always entails a small group size, one may wonder whether the performance of the Bayesian approach is problematic, especially when considering count data? And if so, is the maximum likelihood (ML)-estimator a more adequate alternative? To answer these questions, we perform a simulation study where the performance of the Bayesian approach is compared to the performance of the ML-estimator

Summary

Introduction

The main challenge that we will tackle in this paper lies in the nature of the dyadic measurements obtained from a block or round robin design. We accommodate the family SRM to count outcomes as well. The Bayesian estimator can only be derived using the multilevel framework Such Bayesian approach has already been proposed for the SRM without family roles, where the continuous outcomes are obtained according to a round robin design (Lüdtke, Robitzsch, Kenny, & Trautwein, 2012) and for categorical dyadic measurements (Hoff, 2015), such as count measurements (Koster & Leckie, 2014; Koster, Leckie, Miller, & Hames, 2015). J. Loncke et al, Social Relations Model for Count Data estimation of the SRM without roles, it showed that for continuous outcomes the Bayesian approach can result in biased estimators of the variances for small cluster sizes in combination with small sample sizes (Lüdtke et al, 2012).

Results

Discussion

Conclusion