Integrating Covariates into Social Relations Models: A Plausible Values Approach for Handling Measurement Error in Perceiver and Target Effects

<p>The Social Relations Model (SRM) is a conceptual and analytical approach to examining dyadic behaviors and interpersonal perceptions within groups. In an SRM, the perceiver effect describes a person's tendency to perceive other group members in a certain way, whereas the target effect measures the tendency to be perceived by others in certain ways. In SRM research, it is often of interest to relate these individual SRM effects to covariates. However, the estimated individual SRM effects might not provide a very reliable measure of the true, unobserved SRM effects, resulting in distorted estimates of associations with other variables. This article introduces a plausible values approach that allows users to correct for measurement error when assessing the association of individual SRM effects with other individual difference variables. In the plausible values approach, the latent, true individual SRM effects are treated as missing values and are imputed from an imputation model by applying Bayesian estimation techniques. In a simulation study, the statistical properties of the plausible values approach are compared with two approaches that have been used in previous research. A data example from educational psychology is presented to illustrate how the plausible values approach can be implemented with the software WinBUGS.</p

Supplement to "Multiple Imputation of Missing Covariate Values in Multilevel Models With Random Slopes: A Cautionary Note"

<p>This document provides supplemental materials on our article entitled “Multiple Imputa-<br>tion of Missing Covariate Values in Multilevel Models With Random Slopes: A Cautionary<br>Note”. Supplement A contains details on the different imputation models. Supplement B<br>describes pan’s convergence and autocorrelation behavior. Supplement C contains the imputation procedures that were used in this study. Supplement D contains additional tables.</p> <p> </p

Pooling ANOVA Results from Multiply Imputed Datasets - Supplemental Materials - Example Dataset

<p>Example dataset for the analysis example provided in the online supplemental material of the corresponding article.</p

A Bayesian Approach to More Stable Estimates of Group-Level Effects in Contextual Studies

<div><p>Multilevel analyses are often used to estimate the effects of group-level constructs. However, when using aggregated individual data (e.g., student ratings) to assess a group-level construct (e.g., classroom climate), the observed group mean might not provide a reliable measure of the unobserved latent group mean. In the present article, we propose a Bayesian approach that can be used to estimate a multilevel latent covariate model, which corrects for the unreliable assessment of the latent group mean when estimating the group-level effect. A simulation study was conducted to evaluate the choice of different priors for the group-level variance of the predictor variable and to compare the Bayesian approach with the maximum likelihood approach implemented in the software M<i>plus</i>. Results showed that, under problematic conditions (i.e., small number of groups, predictor variable with a small ICC), the Bayesian approach produced more accurate estimates of the group-level effect than the maximum likelihood approach did.</p></div

A Bayesian Approach for Estimating Multilevel Latent Contextual Models

<p>In many applications of multilevel modeling, group-level (L2) variables for assessing group-level effects are generated by aggregating variables from a lower level (L1). However, the observed group mean might not be a reliable measure of the unobserved true group mean. In this article, we propose a Bayesian approach for estimating a multilevel latent contextual model that corrects for measurement error and sampling error (i.e., sampling only a small number of L1 units from a L2 unit) when estimating group-level effects of aggregated L1 variables. Two simulation studies were conducted to compare the Bayesian approach with the maximum likelihood approach implemented in M<i>plus</i>. The Bayesian approach showed fewer estimation problems (e.g., inadmissible solutions) and more accurate estimates of the group-level effect than the maximum likelihood approach under problematic conditions (i.e., small number of groups, predictor variable with a small intraclass correlation). An application from educational psychology is used to illustrate the different estimation approaches.</p

Exploring Factor Model Parameters across Continuous Variables with Local Structural Equation Models

<p>Using an empirical data set, we investigated variation in factor model parameters across a continuous moderator variable and demonstrated three modeling approaches: multiple-group mean and covariance structure (MGMCS) analyses, local structural equation modeling (LSEM), and moderated factor analysis (MFA). We focused on how to study variation in factor model parameters as a function of continuous variables such as age, socioeconomic status, ability levels, acculturation, and so forth. Specifically, we formalized the LSEM approach in detail as compared with previous work and investigated its statistical properties with an analytical derivation and a simulation study. We also provide code for the easy implementation of LSEM. The illustration of methods was based on cross-sectional cognitive ability data from individuals ranging in age from 4 to 23 years. Variations in factor loadings across age were examined with regard to the age differentiation hypothesis. LSEM and MFA converged with respect to the conclusions. When there was a broad age range within groups and varying relations between the indicator variables and the common factor across age, MGMCS produced distorted parameter estimates. We discuss the pros of LSEM compared with MFA and recommend using the two tools as complementary approaches for investigating moderation in factor model parameters.</p

MOESM1 of Performance decline in low-stakes educational assessments: different mixture modeling approaches

Additional file 1. The Mplus code to analyze the data