A DIAGNOSTIC TOOL FOR CHECKING ASSUMPTIONS OF REGRESSION MIXTURE MODELS

The Impact of Imposing Equality Constraints on Residual Variances Across Classes in Regression Mixture Models

The purpose of this study is to explore the impact of constraining class-specific residual variances to be equal by examining and comparing the parameter estimation of a free model and a constrained model under various conditions. A Monte Carlo simulation study was conducted under several conditions, including the number of predictors, class-specific intercepts, sample size, class-specific regression weights, and class proportion to evaluate the results for parameter estimation of the free model and the restricted model. The free model yielded a more accurate estimation than the restricted model for most of the conditions, but the accuracy of the free model estimation was impacted by the number of predictors, sample size, the disparity in the magnitude of class-specific slopes and intercepts, and class proportion. When equality constraints were imposed in residual variance discrepant conditions, the parameter estimates showed substantial inaccuracy for slopes, intercepts, and residual variances, especially for those in Class 2 (with a lower class-specific slope). When the residual variances were equal between the classes, the restricted model showed better performance under some conditions.

Marginal analysis of bivariate mixed responses with measurement error and misclassification

Bivariate responses with mixed continuous and binary variables arise commonly in applications such as clinical trials and genetic studies. Statistical methods based on jointly modeling continuous and binary variables have been available. However, such methods ignore the effects of response mismeasurement, a ubiquitous feature in applications. It has been well studied that in many settings, ignorance of mismeasurement in variables usually results in biased estimation. In this paper, we consider the setting with a bivariate outcome vector which contains a continuous component and a binary component both subject to mismeasurement. We propose estimating equation approaches to handle measurement error in the continuous response and misclassification in the binary response simultaneously. The proposed estimators are consistent and robust to certain model misspecification, provided regularity conditions. Extensive simulation studies confirm that the proposed methods successfully correct the biases resulting from the error-in-variables under various settings. The proposed methods are applied to analyze the outbred Carworth Farms White mice data arising from a genome-wide association study.

Is Autonomy Always Beneficial for Work Engagement? A Six-year Four-Wave Follow-Up Study

Work engagement is expected to result from job resources such as autonomy. However, previous results have yielded that the autonomy–work engagement relationship is not always particularly strong. Whereas previous longitudinal studies have examined this relationship as an average at a specific point in time, this study examined whether this relationship is different within individuals from one time to another over the years. Furthermore, experiences of work engagement are expected to affect how employees benefit from autonomy, but no studies have so far investigated whether the initial level of work engagement affects the autonomy–work engagement relationship. This study aimed to first identify the different kinds of longitudinal relationship patterns between autonomy and work engagement, and then to investigate whether the identified relationship patterns differ in terms of the initial mean level of work engagement. The four-wave study was conducted among Finnish managers (n = 329) over a period of six years. Multilevel regression mixture analysis identified five relationship patterns. Four of the patterns showed a positive predictive relationship between autonomy and work engagement. However, the relationship was statistically significant in only one of these patterns. Furthermore, when the initial mean level of work engagement was high, autonomy related more strongly to work engagement. However, an atypical pattern was identified that showed a negative association between autonomy and work engagement. In this pattern, the mean level of work engagement was low. Consequently, autonomy may not always enhance work engagement; sometimes this relationship may even be negative.