Causal Latent Class Analysis with Distal Outcomes: A Modified Three-Step Method Using Inverse Propensity Weighting.

Bias-adjusted three-step latent class (LC) analysis is a popular technique for estimating the relationship between LC membership and distal outcomes. Since it is impossible to randomize LC membership, causal inference techniques are needed to estimate causal effects leveraging observational data. This paper proposes two novel strategies that make use of propensity scores to estimate the causal effect of LC membership on a distal outcome variable. Both strategies modify the bias-adjusted three-step approach by using propensity scores in the last step to control for confounding. The first strategy utilizes inverse propensity weighting (IPW), whereas the second strategy includes the propensity scores as control variables. Classification errors are accounted for using the BCH or ML corrections. We evaluate the performance of these methods in a simulation study by comparing it with three existing approaches that also use propensity scores in a stepwise LC analysis. Both of our newly proposed methods return essentially unbiased parameter estimates outperforming previously proposed methods. However, for smaller sample sizes our IPW based approach shows large variability in the estimates and can be prone to non-convergence. Furthermore, the use of these newly proposed methods is illustrated using data from the LISS panel.

Determining differences between therapists using an extended version of the facilitative interpersonal skills performance test.

OBJECTIVES: The therapist-facilitative interpersonal skills (FIS) has shown to predict therapy outcomes, demonstrating that high FIS therapists are more effective than low FIS therapists. There is a need for more insight into the variability in strengths and weaknesses in therapist skills. This study investigates whether a revised and extended FIS-scoring leads to more differentiation in measuring therapists' interpersonal skills. Furthermore, we explorative examine whether subgroups of therapists can be distinguished in terms of differences in their interpersonal responses. METHOD: Using secondary data analysis, 93 therapists were exposed to seven FIS-clips. Responses of therapists using the original and the extended FIS scoring were rated. RESULTS: Three factors were found on the extended FIS scoring distinguishing supportive, expressive, and persuasive interpersonal responses of therapists. A latent profile analysis enlightened the presence of six subgroups of therapists. CONCLUSION: Using the revised and extended FIS-scoring contributes to our understanding of the role of interpersonal skills in the therapeutic setting by unraveling the question what works for whom.

Evaluating Covariate Effects on ESM Measurement Model Changes with Latent Markov Factor Analysis: A Three-Step Approach.

Invariance of the measurement model (MM) between subjects and within subjects over time is a prerequisite for drawing valid inferences when studying dynamics of psychological factors in intensive longitudinal data. To conveniently evaluate this invariance, latent Markov factor analysis (LMFA) was proposed. LMFA combines a latent Markov model with mixture factor analysis: The Markov model captures changes in MMs over time by clustering subjects' observations into a few states and state-specific factor analyses reveal what the MMs look like. However, to estimate the model, Vogelsmeier, Vermunt, van Roekel, and De Roover (2019) introduced a one-step (full information maximum likelihood; FIML) approach that is counterintuitive for applied researchers and entails cumbersome model selection procedures in the presence of many covariates. In this paper, we simplify the complex LMFA estimation and facilitate the exploration of covariate effects on state memberships by splitting the estimation in three intuitive steps: (1) obtain states with mixture factor analysis while treating repeated measures as independent, (2) assign observations to the states, and (3) use these states in a discrete- or continuous-time latent Markov model taking into account classification errors. A real data example demonstrates the empirical value.

The impact of ordinal scales on Gaussian mixture recovery.

Gaussian mixture models (GMMs) are a popular and versatile tool for exploring heterogeneity in multivariate continuous data. Arguably the most popular way to estimate GMMs is via the expectation-maximization (EM) algorithm combined with model selection using the Bayesian information criterion (BIC). If the GMM is correctly specified, this estimation procedure has been demonstrated to have high recovery performance. However, in many situations, the data are not continuous but ordinal, for example when assessing symptom severity in medical data or modeling the responses in a survey. For such situations, it is unknown how well the EM algorithm and the BIC perform in GMM recovery. In the present paper, we investigate this question by simulating data from various GMMs, thresholding them in ordinal categories and evaluating recovery performance. We show that the number of components can be estimated reliably if the number of ordinal categories and the number of variables is high enough. However, the estimates of the parameters of the component models are biased independent of sample size. Finally, we discuss alternative modeling approaches which might be adopted for the situations in which estimating a GMM is not acceptable.

How to explore within-person and between-person measurement model differences in intensive longitudinal data with the R package lmfa.

Intensive longitudinal data (ILD) have become popular for studying within-person dynamics in psychological constructs (or between-person differences therein). Before investigating the dynamics, it is crucial to examine whether the measurement model (MM) is the same across subjects and time and, thus, whether the measured constructs have the same meaning. If the MM differs (e.g., because of changes in item interpretation or response styles), observations cannot be validly compared. Exploring differences in the MM for ILD can be done with latent Markov factor analysis (LMFA), which classifies observations based on the underlying MM (for many subjects and time points simultaneously) and thus shows which observations are comparable. However, the complexity of the method or the fact that no open-source software for LMFA existed until now may have hindered researchers from applying the method in practice. In this article, we provide a step-by-step tutorial for the new user-friendly software package lmfa, which allows researchers to easily perform the analysis LMFA in the freely available software R to investigate MM differences in their own ILD.

Adult lifetime body mass index trajectories and endometrial cancer risk.

OBJECTIVE: To identify body mass index (BMI) trajectories in adult life and to examine their association with endometrial cancer (EC) risk, also exploring whether relations differ by hormonal replacement therapy use. DESIGN: Pooled analysis of two case-control studies. SETTING: Italy and Switzerland. POPULATION: A total of 458 EC cases and 782 controls. METHODS: We performed a latent class growth model to identify homogeneous BMI trajectories over six decades of age, with a polynomial function of age. Odds ratios (ORs) and the corresponding 95% CI for EC risk were derived through a multiple logistic regression model, correcting for classification error. MAIN OUTCOME MEASURES: The relation of BMI trajectories with endometrial cancer. RESULTS: We identified five BMI trajectories. Compared with women in the 'Normal weight-stable' trajectory, a reduction by about 50% in the risk of EC emerged for those in the 'Underweight increasing to normal weight' (95% CI 0.28-0.99). The 'Normal weight increasing to overweight' and the 'Overweight-stable' trajectories were associated with, respectively, an excess of 3% (95% CI 0.66-1.60) and of 71% (95% CI 1.12-2.59) in cancer risk. The OR associated to the trajectory 'Overweight increasing to obese' was 2.03 (95% CI 1.31-3.13). Stronger effects emerged among hormonal replacement therapy never users (OR 2.19 for the 'Overweight-stable' trajectory and OR 2.49 for the 'Overweight increasing to obese' trajectory). CONCLUSIONS: Our study suggests that longer exposure to overweight and obesity across a lifetime is associated with an increased risk of endometrial cancer. Weight during adulthood also appears to play an important role. TWEETABLE ABSTRACT: Longer exposure to overweight and obesity across a lifetime is associated with an increased risk of endometrial cancer.

Identification of Latent Alcohol Use Groups and Transitions over Time Using a 9-Year Follow-Up Study in the Adult General Population.

INTRODUCTION: Studies investigating latent alcohol use groups and transitions of these groups over time are scarce, while such knowledge could facilitate efficient use of screening and preventive interventions for groups with a high risk of problematic alcohol use. Therefore, the present study examines the characteristics, transitions, and long-term stability of adult alcohol use groups and explores some of the possible predictors of the transitions. METHODS: Data were used from the baseline, 3-, 6-, and 9-year follow-up waves of the Netherlands Mental Health Survey and Incidence Study-2 (NEMESIS-2), a representative study of Dutch adults aged 18-64 at baseline (N = 6,646; number of data points: 20,574). Alcohol consumption, alcohol use disorder (AUD), and mental disorders were assessed with the Composite International Diagnostic Interview 3.0. Latent Markov Modelling was used to identify latent groups based on high average alcohol consumption (HAAC) and AUD and to determine transition patterns of people between groups over time (stayers vs. movers). RESULTS: The best fitting model resulted in four latent groups: one nonproblematic group (91%): no HAAC, no AUD; and three problematic alcohol use groups (9%): HAAC, no AUD (5%); no HAAC, often AUD (3%); and HAAC and AUD (1%). HAAC, no AUD was associated with a high mean age (55 years) and low educational level (41%), and no HAAC, often AUD with high proportions of males (78%) and people with high educational level (46%). Eighty-seven percent of all respondents - mostly people with no HAAC, no AUD - stayed in their original group during the whole 9-year period. Among movers, people in a problematic alcohol use group (HAAC and/or AUD) mostly transitioned to another problematic alcohol use group and not to the nonproblematic alcohol use group (no HAAC, no AUD). Explorative analyses suggested that lack of physical activity possibly plays a role in transitions both from and to problematic alcohol use groups over time. CONCLUSION: The detection of three problematic alcohol use groups - with transitions mostly between the different problematic alcohol use groups and not to the group without alcohol problems - points to the need to explicitly address both alcohol consumption and alcohol-related problems (AUD criteria) in screening measures and interventions in order not to miss and to adequately treat all problematic alcohol users. Moreover, explorative findings suggest that prevention measures should also include physical activity.

Scale length does matter: Recommendations for measurement invariance testing with categorical factor analysis and item response theory approaches.

In social sciences, the study of group differences concerning latent constructs is ubiquitous. These constructs are generally measured by means of scales composed of ordinal items. In order to compare these constructs across groups, one crucial requirement is that they are measured equivalently or, in technical jargon, that measurement invariance (MI) holds across the groups. This study compared the performance of scale- and item-level approaches based on multiple group categorical confirmatory factor analysis (MG-CCFA) and multiple group item response theory (MG-IRT) in testing MI with ordinal data. In general, the results of the simulation studies showed that MG-CCFA-based approaches outperformed MG-IRT-based approaches when testing MI at the scale level, whereas, at the item level, the best performing approach depends on the tested parameter (i.e., loadings or thresholds). That is, when testing loadings equivalence, the likelihood ratio test provided the best trade-off between true-positive rate and false-positive rate, whereas, when testing thresholds equivalence, the χ2 test outperformed the other testing strategies. In addition, the performance of MG-CCFA's fit measures, such as RMSEA and CFI, seemed to depend largely on the length of the scale, especially when MI was tested at the item level. General caution is recommended when using these measures, especially when MI is tested for each item individually.

Heterogeneity in Quality of Life of Long-Term Colon Cancer Survivors: A Latent Class Analysis of the Population-Based PROFILES Registry.

BACKGROUND: Long-term colon cancer survivors present heterogeneous health-related quality of life (HRQOL) outcomes. We determined unobserved subgroups (classes) of survivors with similar HRQOL patterns and investigated their stability over time and the association of clinical covariates with these classes. MATERIALS AND METHODS: Data from the population-based PROFILES registry were used. Included were survivors with nonmetastatic (TNM stage I-III) colon cancer (n = 1,489). HRQOL was assessed with the Dutch translation of the European Organisation for Research and Treatment of Cancer Quality of Life Questionnaire C30 version 3.0. Based on survivors' HRQOL, latent class analysis (LCA) was used to identify unobserved classes of survivors. Moreover, latent transition analysis (LTA) was used to investigate changes in class membership over time. Furthermore, the effect of covariates on class membership was assessed using multinomial logistic regression. RESULTS: LCA identified five classes at baseline: class 1, excellent HRQOL (n = 555, 37.3%); class 2, good HRQOL with prevalence of insomnia (n = 464, 31.2%); class 3, moderate HRQOL with prevalence of fatigue (n = 213, 14.3%); class 4, good HRQOL with physical limitations (n = 134, 9.0%); and class 5, poor HRQOL (n = 123, 8.3%). All classes were stable with high self-transition probabilities. Longer time since the diagnosis, no comorbid conditions, and male sex were associated with class 1, whereas older age was associated with class 4. Clinical covariates were not associated with class membership. CONCLUSION: The identified classes are characterized by distinct patterns of HRQOL and can support patient-centered care. LCA and LTA are powerful tools for investigating HRQOL in cancer survivors. IMPLICATIONS FOR PRACTICE: Long-term colon cancer survivors show great heterogeneity in their health-related quality of life. This study identified five distinct clusters of survivors with similar patterns of health-related quality of life and showed that these clusters remain stable over time. It was also shown that these clusters do not significantly differ in tumor characteristics or received treatment. Cluster membership of long-term survivors can be identified by sociodemographic characteristics but is not predetermined by diagnosis and treatment.

Dietary patterns and oral and pharyngeal cancer using latent class analysis.

The methods traditionally used to identify a posteriori dietary patterns are principal components, factor and cluster analysis. The aim of our study is to assess the relationship between dietary patterns derived with latent class analysis (LCA) and oral/pharyngeal cancer risk (OPC), highlighting the strengths of this method compared to traditional ones. We analyzed data from an Italian multicentric case-control study on OPC including 946 cases and 2,492 hospital controls. Dietary patterns were derived using LCA on 25 food groups. A multiple logistic regression model was used to derive odds ratios (ORs) and corresponding 95% confidence intervals (CIs) for OPC according to the dietary patterns identified. We identified four dietary patterns. The first one was characterized by a high intake of leafy and fruiting vegetable and fruits (Prudent pattern), the second one showed a high intake of red meat and low intake of selected fruits and vegetables (Western pattern). The last two patterns showed a combination-type of diet. We labeled "Lower consumers-combination pattern" the cluster that showed a low intake of the majority of foods, and "Higher consumers-combination pattern" the one characterized by a high intake of various foods. Compared to the "Prudent pattern", the "Western" and the "Lower consumers-combination" ones were positively related to the risk of OPC (OR = 2.56, 95% CI: 1.90-3.45 and OR = 2.23, 95% CI: 1.64-3.02). No difference in risk emerged for the "Higher consumers-combination pattern" (OR = 1.28, 95% CI: 0.92-1.77).

Repeated measures regression mixture models.

Regression mixture models are one increasingly utilized approach for developing theories about and exploring the heterogeneity of effects. In this study we aimed to extend the current use of regression mixtures to a repeated regression mixture method when repeated measures, such as diary-type and experience-sampling method, data are available. We hypothesized that additional information borrowed from the repeated measures would improve the model performance, in terms of class enumeration and accuracy of the parameter estimates. We specifically compared three types of model specifications in regression mixtures: (a) traditional single-outcome model; (b) repeated measures models with three, five, and seven measures; and (c) a single-outcome model with the average of seven repeated measures. The results showed that the repeated measures regression mixture models substantially outperformed the traditional and average single-outcome models in class enumeration, with less bias in the parameter estimates. For sample size, whereas prior recommendations have suggested that regression mixtures require samples of well over 1,000 participants, even for classes at a large distance from each other (classes with regression weights of .20 vs. .70), the present repeated measures regression mixture models allow for samples as low as 200 participants with an increased number (i.e., seven) of repeated measures. We also demonstrate an application of the proposed repeated measures approach using data from the Sleep Research Project. Implications and limitations of the study are discussed.

Bayesian Multilevel Latent Class Models for the Multiple Imputation of Nested Categorical Data.

With this article, we propose using a Bayesian multilevel latent class (BMLC; or mixture) model for the multiple imputation of nested categorical data. Unlike recently developed methods that can only pick up associations between pairs of variables, the multilevel mixture model we propose is flexible enough to automatically deal with complex interactions in the joint distribution of the variables to be estimated. After formally introducing the model and showing how it can be implemented, we carry out a simulation study and a real-data study in order to assess its performance and compare it with the commonly used listwise deletion and an available R-routine. Results indicate that the BMLC model is able to recover unbiased parameter estimates of the analysis models considered in our studies, as well as to correctly reflect the uncertainty due to missing data, outperforming the competing methods.

On the Development of Harmony, Turbulence, and Independence in Parent-Adolescent Relationships: A Five-Wave Longitudinal Study.

The separation-individuation, evolutionary, maturational, and expectancy violation-realignment perspectives propose that the relationship between parents and adolescents deteriorate as adolescents become independent. This study examines the extent to which the development of adolescents' perceived relationship with their parents is consistent with the four perspectives. A latent transition analysis was performed in a two-cohort five-wave longitudinal study design covering ages 12-16 (n = 919, 49.2% female) and 16-20 (n = 392, 56.6% female). Generally, from 12 to 16 year adolescents moved away from parental authority and perceived increasing conflicts with their parents, whereas from 16 to 20 years adolescents perceived independence and improved their relationships with parents. Hereby, we also identified substantial patterns of individual differences. Together, these general and individual patterns provide fine-grained insights in relationship quality development.

Statistical power of likelihood ratio and Wald tests in latent class models with covariates.

This paper discusses power and sample-size computation for likelihood ratio and Wald testing of the significance of covariate effects in latent class models. For both tests, asymptotic distributions can be used; that is, the test statistic can be assumed to follow a central Chi-square under the null hypothesis and a non-central Chi-square under the alternative hypothesis. Power or sample-size computation using these asymptotic distributions requires specification of the non-centrality parameter, which in practice is rarely known. We show how to calculate this non-centrality parameter using a large simulated data set from the model under the alternative hypothesis. A simulation study is conducted evaluating the adequacy of the proposed power analysis methods, determining the key study design factor affecting the power level, and comparing the performance of the likelihood ratio and Wald test. The proposed power analysis methods turn out to perform very well for a broad range of conditions. Moreover, apart from effect size and sample size, an important factor affecting the power is the class separation, implying that when class separation is low, rather large sample sizes are needed to achieve a reasonable power level.

Regression Mixture Models: Does Modeling the Covariance Between Independent Variables and Latent Classes Improve the Results?

Regression mixture models are increasingly used as an exploratory approach to identify heterogeneity in the effects of a predictor on an outcome. In this simulation study, we tested the effects of violating an implicit assumption often made in these models; that is, independent variables in the model are not directly related to latent classes. Results indicate that the major risk of failing to model the relationship between predictor and latent class was an increase in the probability of selecting additional latent classes and biased class proportions. In addition, we tested whether regression mixture models can detect a piecewise relationship between a predictor and outcome. Results suggest that these models are able to detect piecewise relations but only when the relationship between the latent class and the predictor is included in model estimation. We illustrate the implications of making this assumption through a reanalysis of applied data examining heterogeneity in the effects of family resources on academic achievement. We compare previous results (which assumed no relation between independent variables and latent class) to the model where this assumption is lifted. Implications and analytic suggestions for conducting regression mixture based on these findings are noted.

Hidden Markov Item Response Theory Models for Responses and Response Times.

Current approaches to model responses and response times to psychometric tests solely focus on between-subject differences in speed and ability. Within subjects, speed and ability are assumed to be constants. Violations of this assumption are generally absorbed in the residual of the model. As a result, within-subject departures from the between-subject speed and ability level remain undetected. These departures may be of interest to the researcher as they reflect differences in the response processes adopted on the items of a test. In this article, we propose a dynamic approach for responses and response times based on hidden Markov modeling to account for within-subject differences in responses and response times. A simulation study is conducted to demonstrate acceptable parameter recovery and acceptable performance of various fit indices in distinguishing between different models. In addition, both a confirmatory and an exploratory application are presented to demonstrate the practical value of the modeling approach.

Power Analysis for the Likelihood-Ratio Test in Latent Markov Models: Shortcutting the Bootstrap p-Value-Based Method.

The latent Markov (LM) model is a popular method for identifying distinct unobserved states and transitions between these states over time in longitudinally observed responses. The bootstrap likelihood-ratio (BLR) test yields the most rigorous test for determining the number of latent states, yet little is known about power analysis for this test. Power could be computed as the proportion of the bootstrap p values (PBP) for which the null hypothesis is rejected. This requires performing the full bootstrap procedure for a large number of samples generated from the model under the alternative hypothesis, which is computationally infeasible in most situations. This article presents a computationally feasible shortcut method for power computation for the BLR test. The shortcut method involves the following simple steps: (1) obtaining the parameters of the model under the null hypothesis, (2) constructing the empirical distributions of the likelihood ratio under the null and alternative hypotheses via Monte Carlo simulations, and (3) using these empirical distributions to compute the power. We evaluate the performance of the shortcut method by comparing it to the PBP method and, moreover, show how the shortcut method can be used for sample-size determination.

Stepwise Latent Class Models for Explaining Group-Level Outcomes Using Discrete Individual-Level Predictors.

Explaining group-level outcomes from individual-level predictors requires aggregating the individual-level scores to the group level and correcting the group-level estimates for measurement errors in the aggregated scores. However, for discrete variables it is not clear how to perform the aggregation and correction. It is shown how stepwise latent class analysis can be used to do this. First, a latent class model is estimated in which the scores on a discrete individual-level predictor are used to construct group-level latent classes. Second, this latent class model is used to aggregate the individual-level predictor by assigning the groups to the latent classes. Third, a group-level analysis is performed in which the aggregated measures are related to the remaining group-level variables while correcting for the measurement error in the class assignments. This stepwise approach is introduced in a multilevel mediation model with a single individual-level mediator, and compared to existing methods in a simulation study. We also show how a mediation model with multiple group-level latent variables can be used with multiple individual-level mediators and this model is applied to explain team productivity (group level) as a function of job control (individual level), job satisfaction (individual level), and enriched job design (group level).

Latent class bivariate model for the meta-analysis of diagnostic test accuracy studies.

BACKGROUND: Several types of statistical methods are currently available for the meta-analysis of studies on diagnostic test accuracy. One of these methods is the Bivariate Model which involves a simultaneous analysis of the sensitivity and specificity from a set of studies. In this paper, we review the characteristics of the Bivariate Model and demonstrate how it can be extended with a discrete latent variable. The resulting clustering of studies yields additional insight into the accuracy of the test of interest. METHODS: A Latent Class Bivariate Model is proposed. This model captures the between-study variability in sensitivity and specificity by assuming that studies belong to one of a small number of latent classes. This yields both an easier to interpret and a more precise description of the heterogeneity between studies. Latent classes may not only differ with respect to the average sensitivity and specificity, but also with respect to the correlation between sensitivity and specificity. RESULTS: The Latent Class Bivariate Model identifies clusters of studies with their own estimates of sensitivity and specificity. Our simulation study demonstrated excellent parameter recovery and good performance of the model selection statistics typically used in latent class analysis. Application in a real data example on coronary artery disease showed that the inclusion of latent classes yields interesting additional information. CONCLUSIONS: Our proposed new meta-analysis method can lead to a better fit of the data set of interest, less biased estimates and more reliable confidence intervals for sensitivities and specificities. But even more important, it may serve as an exploratory tool for subsequent sub-group meta-analyses.

Short-term memory development: differences in serial position curves between age groups and latent classes.

In studies on the development of cognitive processes, children are often grouped based on their ages before analyzing the data. After the analysis, the differences between age groups are interpreted as developmental differences. We argue that this approach is problematic because the variance in cognitive performance within an age group is considered to be measurement error. However, if a part of this variance is systematic, it can provide very useful information about the cognitive processes used by some children of a certain age but not others. In the current study, we presented 210 children aged 5 to 12 years with serial order short-term memory tasks. First we analyze our data according to the approach using age groups, and then we apply latent class analysis to form latent classes of children based on their performance instead of their ages. We display the results of the age groups and the latent classes in terms of serial position curves, and we discuss the differences in results. Our findings show that there are considerable differences in performance between the age groups and the latent classes. We interpret our findings as indicating that the latent class analysis yielded a much more meaningful way of grouping children in terms of cognitive processes than the a priori grouping of children based on their ages.