Modeling predictors of latent classes in regression mixture models

The purpose of this study is to provide guidance on a process for including latent class predictors in regression mixture models. We first examine the performance of current practice for using the 1-step and 3-step approaches where the direct covariate effect on the outcome is omitted. None of the approaches show adequate estimates of model parameters. Given that Step 1 of the 3-step approach shows adequate results in class enumeration, we suggest using an alternative approach: (a) decide the number of latent classes without predictors of latent classes, and (b) bring the latent class predictors into the model with the inclusion of hypothesized direct covariate effects. Our simulations show that this approach leads to good estimates for all model parameters. The proposed approach is demonstrated by using empirical data to examine the differential effects of family resources on students’ academic achievement outcome. Implications of the study are discussed

Impact of an equality constraint on the class-specific residual variances in regression mixtures:a Monte Carlo simulation study

Regression mixture models are a novel approach to modeling the heterogeneous effects of predictors on an outcome. In the model-building process, often residual variances are disregarded and simplifying assumptions are made without thorough examination of the consequences. In this simulation study, we investigated the impact of an equality constraint on the residual variances across latent classes. We examined the consequences of constraining the residual variances on class enumeration (finding the true number of latent classes) and on the parameter estimates, under a number of different simulation conditions meant to reflect the types of heterogeneity likely to exist in applied analyses. The results showed that bias in class enumeration increased as the difference in residual variances between the classes increased. Also, an inappropriate equality constraint on the residual variances greatly impacted on the estimated class sizes and showed the potential to greatly affect the parameter estimates in each class. These results suggest that it is important to make assumptions about residual variances with care and to carefully report what assumptions are made

Using multilevel regression mixture models to identify level-1 heterogeneity in level-2 effects

This article proposes a novel exploratory approach for assessing how the effects of Level-2 predictors differ across Level-1 units. Multilevel regression mixture models are used to identify latent classes at Level 1 that differ in the effect of 1 or more Level-2 predictors. Monte Carlo simulations are used to demonstrate the approach with different sample sizes and to demonstrate the consequences of constraining 1 of the random effects to 0. An application of the method to evaluate heterogeneity in the effects of classroom practices on students is used to show the types of research questions that can be answered with this method and the issues faced when estimating multilevel regression mixtures

Predicting Individual Treatment Effects: Challenges and Opportunities for Machine Learning and Artificial Intelligence

Personalized medicine seeks to identify the right treatment for the right patient at the right time. Predicting the treatment effect for an individual patient has the potential to transform treatment of patients and drastically improve patients outcomes. In this work, we illustrate the potential for ML and AI methods to yield useful predictions of individual treatment effects. Using the predicted individual treatment effects (PITE) framework which uses baseline covariates (features) to predict whether a treatment is expected to yield benefit for a given patient compared to an alternative intervention we provide an illustration of the potential of such approaches and provide a detailed discussion of opportunities for further research and open challenges when seeking to predict individual treatment effects

Evaluating differential effects using regression interactions and regression mixture models

Research increasingly emphasizes understanding differential effects. This article focuses on understanding regression mixture models, which are relatively new statistical methods for assessing differential effects by comparing results to using an interactive term in linear regression. The research questions which each model answers, their formulation, and their assumptions are compared using Monte Carlo simulations and real data analysis. The capabilities of regression mixture models are described and specific issues to be addressed when conducting regression mixtures are proposed. The article aims to clarify the role that regression mixtures can take in the estimation of differential effects and increase awareness of the benefits and potential pitfalls of this approach. Regression mixture models are shown to be a potentially effective exploratory method for finding differential effects when these effects can be defined by a small number of classes of respondents who share a typical relationship between a predictor and an outcome. It is also shown that the comparison between regression mixture models and interactions becomes substantially more complex as the number of classes increases. It is argued that regression interactions are well suited for direct tests of specific hypotheses about differential effects and regression mixtures provide a useful approach for exploring effect heterogeneity given adequate samples and study design

Accelerometry cut points for physical activity in underserved African Americans

Background: Despite their increased use, no studies have examined the validity of Actical accelerometry cut points for moderate physical activity (PA) in underserved (low-income, high-crime), minority populations. The high rates of chronic disease and physical inactivity in these populations likely impact the measurement of PA. There is growing concern that traditionally defined cut points may be too high for older or inactive adults. The present study aimed to determine the self-selected pace associated with instructions to walk for exercise and the corresponding accelerometry estimates (e.g. Actical counts/minute) for underserved, African American adults. Method: Fifty one participants (61% women) had a mean age of 60.1 (SD=9.9) and a mean body mass index of 30.5 kg/m2 (SD=60). They performed one seated task, on standing task, and three walking tasks: strolling ; walking for exercise ; and walking in an emergency. Results: The average pace for strolling, walking for exercise, and walking in an emergency were 1.62 miles per hour (mph; SD=.51), 2.51 mph (SD=.53), and 2.86 mph (SD=.58), respectively. Regression analyses showed that the predicted counts/minute for a pace of 2.0 mph (which is used as the criterion for moderate exercise in this study) was 1075 counts/minute (SEM=73). Conclusions: The cut point associated with subjectively determined moderate PA is similar to those previously published for older adults and extends to the use of adjusted cut points to African American populations. These results indicate that accurate cut points can be obtained using this innovative methodology

The effects of sample size on the estimation of regression mixture models

Regression mixture models are a statistical approach used for estimating heterogeneity in effects. This study investigates the impact of sample size on regression mixture’s ability to produce “stable” results. Monte Carlo simulations and analysis of resamples from an application data set were used to illustrate the types of problems that may occur with small samples in real data sets. The results suggest that (a) when class separation is low, very large sample sizes may be needed to obtain stable results; (b) it may often be necessary to consider a preponderance of evidence in latent class enumeration; (c) regression mixtures with ordinal outcomes result in even more instability; and (d) with small samples, it is possible to obtain spurious results without any clear indication of there being a problem