A strength of the method is the ability to conveniently estimate models for many groups. The method is a valuable alternative to the currently used multiple-group CFA methods for studying measurement invariance that require multiple manual model adjustments guided by modifica- tion indexes.
Multiple-group CFA is not practical with many groups due to poor model fit of the scalar model and too many large modification indexes. In contrast, the alignment method is based on the configural model and essentially automates and greatly simplifies measurement invariance analysis.
The method also provides a detailed account of parameter invariance for every model parameter in every group. IRT studies of many groups: The alignment method. A strength of the method is the ability to conveniently estimate models for many groups, such as with comparisons of countries. This paper focuses on IRT applications of the alignment method. An empirical investigation is made of binary knowledge items administered in two separate surveys of a set of countries.
A Monte Carlo study is presented that shows how the quality of the alignment can be assessed. Disentangling shape from levels effects in person- centered analyses: An illustration based university teacher multidimensional profiles of effectiveness. Doubly latent multilevel analyses of classroom climate: An illustration. The Journal of Experimental Education. Mixture class recovery in GMM under varying degrees of class separation: Frequentist versus Bayesian estimation.
Psychological Methods, 18 2 , The aim of the current article was to explore the impact of latent class separation i. The main goal was to provide insight about the optimal estimation condition under different degrees of latent class separation for GMM. Maximum likelihood and the remaining Bayesian estimation conditions yielded poor parameter recovery for the latent class proportions and the growth trajectories.
A genome-wide association study of a sustained pattern of antidepressant response. Journal of Psychiatric Research, 47 9 , A latent markov modelling approach to the evaluation of circulating cathodic antigen strips for schistosomiasis diagnosis pre- and post-Praziquantel treatment in Uganda.
PLoS Comput Biol 9 12 : e With the recent resolution on schistosomiasis elimination by the 65th World Health Assembly, appropriate diagnostic tools to inform interventions are keys to their success. We present a discrete Markov chains modelling framework that deals with the longitudinal study design and the measurement error in the diagnostic methods under study. The aim was to evaluate the diagnostic accuracy of Circulating Cathodic Antigen CCA and of double Kato-Katz KK faecal slides over three consecutive days for Schistosoma mansoni infection simultaneously by age group at baseline and at two follow-up times post treatment.
Diagnostic test sensitivities and specificities and the true underlying infection prevalence over time as well as the probabilities of transitions between infected and uninfected states are provided. The estimated transition probability matrices provide parsimonious yet important insights into the re-infection and cure rates in the two age groups. We show that the CCA diagnostic performance remained constant after PZQ treatment and that this test was overall more sensitive but less specific than single-day double KK for the diagnosis of S.
The probability of clearing infection from baseline to 9 weeks was higher among those who received two PZQ doses compared to one PZQ dose for both age groups, with much higher re-infection rates among children compared to adolescents and adults. We recommend LMMs as a useful methodology for monitoring and evaluation and treatment decision research as well as CCA for mapping surveys of S.
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Analyzing latent state-trait and multiple-indicator latent growth curve models as multilevel structural equation models. Frontiers in Psychology, 4, Although it is well-known that standard single-indicator LGC models can be analyzed within either the structural equation modeling SEM or multilevel ML; hierarchical linear modeling frameworks, few researchers realize that LST and multivariate LGC models, which use multiple indicators at each time point, can also be specified as ML models.
Despite the practical advantages of the ML-SEM approach under these circumstances, there are also some limitations that researchers should consider. The posted version corrects several typos in the published version. An earlier version of this paper was posted as web note A 3-step method for latent class predictor variables is studied in several different settings including latent class analysis, latent transition analysis, and growth mixture modeling. It is explored under violations of its assumptions such as with direct effects from predictors to latent class indicators.
The 3-step method is also considered for distal variables. The Lanza et al. Standard errors are also developed for the Lanza method since these were not given in Lanza et al. Latent class analysis and finite mixture nodeling. Nathan and T. Little Eds. New York, NY. Oxford University Press. Multivariate Behavioral Research, Nonetheless, this literature has historically been diffuse, with different notations, motivations, and parameterizations making mixture models appear disconnected.
This pedagogical review facilitates an integrative understanding of mixture models. First, 5 proto- typic mixture models are presented in a unified format with incremental complexity while highlighting their mutual reliance on familiar probability laws, common assumptions, and shared aspects of interpretation. Both relax a key assumption of classic mixture models but do so in different ways. Similarities in construction and interpretation among hybrid mixtures and among parallel-process mixtures are emphasized.
Third, the combination of both extensions is motivated and illustrated by means of an example on oppositional defiant and depressive symptoms. By clarifying how existing mixture models relate and can be combined, this article bridges past and current developments and provides a foundation for understanding new developments. An ACE in the hole: Twin family models for applied behavioral genetics research.
The Leadership Quarterly, 24 4 , Growth Curve Models with Categorical Outcomes. In Encyclopedia of Criminology and Criminal Justice pp. Grimm , Joel S. Nesselroade Exploratory latent growth models in the structural equation modeling framework. This confirmatory approach is appropriate when a strong theory guides the model fitting process. However, this approach is often also used when there is not a strong theory to guide the model fitting process, which might lead researchers to misrepresent or miss key change characteristics present in their data.
We discuss Tuckerized curves Tucker, , as an exploratory way of modeling change processes based on principal components analysis and propose an exploratory approach to latent growth modeling whereby minimal constraints are imposed on the structure of within-person change. These methods are applied to longitudinal data on cortisol response during a controlled experimental manipulation and height changes from early childhood through adulthood collected from 2 different studies.
We highlight the additional insights gained, some of the benefits, limitations, and potential extensions of the exploratory growth curve approach and suggest there is much to be gained from using such models to generate new and potentially more precise theories about change and development.
Are commitment profiles stable and predictable? A latent transition analysis. The primary goal of the current study was to use Latent Profile Analysis LPA and Latent Transition Analysis LTA to identify profile groups and examine changes in profile membership over an 8- month period in an organization undergoing a strategic change. We found that commitment profiles have substantial temporal stability and that trustworthiness positively predicts memberships in more desirable commitment profiles. There was also some, albeit weak, evidence that changes in perceived trustworthiness were accompanied by corresponding shifts in the commitment profile.
Factor analysis of the hospital depression and anxiety scale: A Bayesian structural equation modeling approach. Quality of Life Research, However, the overly restrictive assumption of exact zero cross-loadings and residual correlations in ML-CFA can lead to poor model fits and distorted factor structures. BSEM specified approximate zero cross-loadings and residual correlations through the use of zero-mean, small-variance informative priors.
The model comparison was based on the Bayesian information criterion BIC. The BSEM two- factor model with approximate zero cross-loadings and residual correlations fitted both samples well with the lowest BIC of the three models and displayed a simple and parsimonious factor-loading pattern. Conclusions: The study demonstrated that the two-factor structure fitted the HADS well, suggesting its usefulness in assessing the symptoms of anxiety and depression in clinical practice.
BSEM is a sophisticated and flexible statistical technique that better reflects substantive theories and locates the source of model misfit. Future use of BSEM is recom- mended to evaluate the latent structure of other psycholog- ical instruments. Single and multiple ability estimation in the SEM framework: A non-informative Bayesian estimation approach. Prince, M. The clinical course of alcohol use disorders: Using joinpoint analysis to aid in interpretation of growth mixture models.
Drug and Alcohol Dependence. One approach to modeling this heterogeneity is latent growth mixture modeling LGMM , which identi? LGMM is data-driven and uses an iterative process of testing a sequential number researcher-selected of latent subgroups then selecting the best? Despite the advantages of LGMM e.
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Joinpoint analysis JPA is a data analysis procedure that is used to identify discrete change points in longitudinal data e. Results: Results from this secondary data analysis of AUD participants participating in the NIAAA sponsored relapse replication and extension project uncovered four latent classes of drinking trajectories. Embedding multilevel survival analysis of dyadic social interaction in structural equation models: Hazard rates as both outcomes and predictors.
This same pattern will predict increases in future antisocial behavior. Less child positive and more child neutral given parent negative predicted increases in third-grade antisocial behavior. Conclusions The model is a useful analytic tool for studying rates of social behavior. Lack of positive affect or excess neutral affect may be a new risk factor for child antisocial behavior.
A gentle introduction to Bayesian analysis: Applications to research in child development. Child Development. In this study a gentle introduction to Bayesian analysis is provided. It is shown under what circumstances it is attrac- tive to use Bayesian estimation, and how to interpret properly the results. First, the ingredients underlying Bayesian methods are introduced using a simplifed example. Thereafter, the advantages and pitfalls of the specification of prior knowledge are discussed.
To illustrate Bayesian methods explained in this study, in a second example a series of studies that examine the theoretical framework of dynamic interactionism are considered. In the Discussion the advantages and disadvantages of using Bayesian statistics are reviewed, and guidelines on how to report on Bayesian statistics are provided. Choosing between Scylla and Charybdis? A comparison of scalar, partial and the novel possibility of approximate measurement invariance.
They showed that with BSEM exact zeros constraints can be replaced with approximate zeros to allow for minimal steps away from strict MI, still yielding a well-fitting model. This new opportunity enables researchers to make explicit trade-offs between the degree of MI on the one hand, and the degree of model fit on the other. Throughout the paper we discuss the topic of approximate MI, followed by an empirical illustration where the test for MI fails, but where allowing for approximate MI results in a well-fitting model.
Using simulated data, we investigate in which situations approximate MI can be applied and when it leads to unbiased results. In the discussion we provide a step-by-step guide in which situation what type of MI is preferred. Our paper provides a first step in the new research area of partial approximate MI and shows that it can be a good alternative when strict MI leads to a badly fitting model and when partial MI cannot be applied.
Bayesian estimation and inference: A user's guide. The foundations of Bayesian estimation and inference are first reviewed. Data are available from the first author, code for the program Mplus is provided, and tables illustrate how to present Bayesian results. In conclusion, the many benefits and few hindrances of Bayesian methods are discussed, where the major hindrance has been an easily solvable lack of familiarity by organizational researchers.
New approaches for examining associations with latent categorical variables: Applications to substance abuse and aggression. Psychology of Addictive Behaviors. When the categorical variable is latent e. However, recent simulation studies have found that this classical three-step analysis championed by the pioneers of LCA produces underestimates of the associations of latent classes with other variables. The purpose of this article is to dissuade researchers from conducting classical three-step analysis and to promote the use of the two newer approaches that are described and compared.
Modeling nonlinear change via latent change and latent acceleration frameworks: Examining velocity and acceleration of growth trajectories. We highlight the additional information gained from fitting growth curves in these frameworks as well as limitations and extensions of these approaches. Simple measures and complex structures: Is it worth employing a more complex model of personality in Big Five inventories?
Journal of Research in Personality. The question arises as to what impact the application of either method has on the construct validity of personality inventories. Generally, scores derived from either method did not differ substantially. When applying ESEM, convergent validity declined but discriminant validity improved. When applying CFA, convergent and discriminant validity decreased. We conclude that using current personality questionnaires that utilize a simple structure is appropriate. Pages: DOI: The purpose of this article is to provide a tutorial for perform- ing structural equation modeling analyses of cross-sectional and longitudinal models for mixed independent variable dyadic data, and to clarify questions regarding various dyadic data analysis specifications that have not been addressed elsewhere.
Artificially generated data similar to the Newlywed Project and the Swedish Adoption Twin Study on Aging were used to illustrate analysis models for distinguishable and indistinguishable dyads, respectively. Due to their widespread use among applied researchers, the AMOS and Mplus statistical analysis software packages were used to analyze the dyadic data structural equation models illustrated here. These analysis models are presented in sufficient detail to allow researchers to perform these analyses using their preferred statistical analysis software package.
Harring : Modeling growth in latent variables using a piecewise function. As an extension of this framework, this research study considers a piecewise function for describing segmented change of a latent construct over time where the latent construct is itself measured by multiple indicators gathered at each measurement occasion. The time of transition from one phase to another is not known a priori and thus is a parameter to be estimated.
Utility of the model is highlighted in 2 ways. First, a small Monte Carlo simulation is executed to show the ability of the model to recover true known growth parameters, including the location of the point of transition or knot , under different manipulated condi- tions. Second, an empirical example using longitudinal reading data is fitted via maximum likelihood and results discussed. Mplus Version 6. Using a nonparametric multilevel latent markov model to evaluate diagnostics for trachoma.
Although high-performance tests are desirable, increased accuracy is frequently accompanied by a requirement for more elaborate infrastructure, which is often not feasible in the developing world. These challenges are pertinent to mapping, impact monitoring, and surveillance in trachoma elimination programs.
Estimates were obtained by using data collected before and after mass azithromycin administration. Estimated transition probabilities provide useful insights into key epidemiologic questions about the persistence of disease and the clearance of infection as well as the required frequency of surveillance in the postelimination setting. Chapter Exploratory Structural Equation Modeling. In Hancock, G. Structural equation modeling: A second course 2nd ed.
Supplementary materials used in this chapter can be found here and here. BSEM measurement invariance analysis. A BSEM Bayesian Structural Equation Modeling approach is proposed for detecting non-invariance that is similar to modification indices with maximum-likelihood estimation, but unlike maximum-likelihood is applicable also for high-dimensional latent variable models for categorical variables. Under certain forms of non-invariance, BSEM gives proper comparisons of factor means and variances using only approximate measurement invariance and without relaxing the invariance specifications or deleting non-invariant items.
To ensure correct estimation, a two-step Bayesian analysis procedure is proposed, where step 1 uses BSEM to identify non-invariant parameters and step 2 frees those parameters. Missing data in substance abuse treatment research: Current methods and modern approaches. Compliance mixture modelling with a zero effect complier class and missing data.
Biometrics, 68, The intent to treat estimand ITT measures the effect of treatment assignment, but not the effect of treatment if subjects take treatments to which they are not assigned. The desire to estimate the efficacy of the treatment in this case has been the impetus for a substantial literature on compliance over the last 15 years. In papers dealing with this issue, it is typically assumed there are different types of subjects, for example, those who will follow treatment assignment compliers , and those who will always take a particular treatment irrespective of treatment assignment.
The estimands of primary interest are the complier proportion and the complier average treatment effect CACE. To estimate CACE, researchers have used various methods, for example, instrumental variables and parametric mixture models, treating compliers as a single class. However, it is often unreasonable to believe all compliers will be affected. This paper therefore treats compliers as a mixture of two types, those belonging to a zero effect class, others to an effect class.
Second, in most experiments, some subjects drop out or simply do not report the value of the outcome variable, and the failure to take into account missing data can lead to biased estimates of treatment effects. Recent work on compliance in randomized experiments has addressed this issue by assuming missing data are missing at random or latently ignorable. We extend this work to the case where compliers are a mixture of types and also examine alternative types of non-ignorable missing data assumptions.
Psychological Assessment. Advance online publication. In each of these cases, I show that the response processes can be measured via pseudoitems derived from the observed responses. The estimation of these models via standard software programs that allow for missing data is also discussed. The article concludes with two detailed applications that illustrate the prevalence of multiple response processes.
Behavioral Research Methods, Advance online publication. Likert scales , items can be presented in a comparative fashion, so that respondents are asked to rank the items within blocks forced-choice format. However, classical scoring procedures for these forced-choice designs lead to ipsative data, which presents psychometric challenges that are well described in the literature.
Estimation and scoring is performed using Mplus, and a very straightforward Excel macro is provided that writes full Mplus input files for any forced-choice design. Armed with these tools, using a forced-choice design is now as easy as using ratings. A comparison of four approaches to account for method effects in latent state-trait analyses. Most LST applications use multiple repeatedly measured observed variables as indicators of latent trait and latent state residual factors. In practice, such indicators often show shared indicator-specific or method variance over time.
In this article, the authors compare 4 approaches to account for such method effects in LST models and discuss the strengths and weaknesses of each approach based on theoretical considerations, simulations, and applications to actual data sets. Recommendations for the choice of an appropriate model are provided. How few countries will do? Comparative survey analysis from a Bayesian perspective. Survey Research Methods, , The authors concluded that a sample of 50 to countries is needed for accurate estimation. Recently, Bayesian estimation methods have been introduced in structural equation modeling which should work well with much lower sample sizes.
The current study reanalyzes the simulation of Meuleman and Billiet using Bayesian estimation to find the lowest number of countries needed when conducting multilevel SEM. The main result of our simulations is that a sample of about 20 countries is sufficient for accurate Bayesian estimation, which makes multilevel SEM practicable for the number of countries commonly available in large scale comparative surveys.
We evaluated three tests for viable infection: detection of parasite specific DNA Dra1 fragments, haematuria and presence of parasite eggs for sensitivity Se and specificity Sp. Methods: Over urine specimens collected from adult volunteers in an endemic area in Western Nigeria were assessed for haematuria then filtered in the field, the filter papers dried and later examined for eggs and DNA.
The results were stratified according to sex and age and subjected to Latent Class analysis.
Dra1 became undetectable 2 weeks after praziquantel treatment. We conclude detection of Dra1 fragment is a definitive test for the presence of Schistosoma haematobium infection. Initiation and persistence of alcohol use in United States Black, Hispanic, and White male and female youth. Addictive Behaviors, 37, However, the degree that alcohol use persists, which is often a necessary cause for developing alcohol-related problems or an alcohol use disorder, is not well studied, particularly with attention to race and gender.
A novel statistical approach, the Multi-facet Longitudinal Model, enables the concurrent study of age of initiation and persistence. Methods: The models were applied to longitudinal data on youth alcohol use fromages 12 through 19, collected in the U. Results: Results confirmed that Black adolescents initiate alcohol use at later ages than doWhite youth.
Further, after initiation, White adolescents were substantially more likely than Black adolescents to continue reporting alcohol use in subsequent years. Hispanic teens showed an intermediate pattern. Gender differences were more ambiguous, with a tendency for boys to be less likely to continue drinking after initiation than were girls. Conclusions: Novel findings from the new analytic models suggest differential implications of early alcohol use by race and gender. Early use of alcohol might be less consequential for males who initiate alcohol use early, Black, and Hispanic youth than for their female and White counterparts.
Measurement invariance of big-five factors over the life span: ESEM tests of gender, age, plasticity, maturity, and La Dolce Vita effects. Developmental Psychology.
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Confirmatory factor analyses CFAs conducted at the item level often do not support a priori FFA structures, due in part to the overly restrictive assumptions of CFA models. ESEM fitted the data substantially better and resulted in much more differentiated less correlated factors than did CFA. Methodologically, we extended ESEM introducing ESEM-within-CFA models and a hybrid of multiple groups and multiple indicators multiple causes models , evaluating full measurement invariance and latent mean differences over age, gender, and their interaction.
Substantively the results showed that women had higher latent scores for all Big Five factors except for Openness and that these gender differences were consistent over the entire life span. Substantial nonlinear age effects led to the rejection of the plaster hypothesis and the maturity principle but did support a newly proposed la dolce vita effect in old age. In later years, individuals become happier more agreeable and less neurotic , more self-content and self-centered less extroverted and open , more laid back and satisfied with what they have less conscientious, open, outgoing and extroverted , and less preoccupied with productivity.
Bayesian SEM: A more flexible representation of substantive theory. Psychological Methods, 17, Click ""download paper"" below for the latest version of October 21, Download the 2nd version dated April 14, Click here to view the seven web tables referred to in the paper and here to view Mplus inputs, data, and outputs used in this version of paper.
Download the 1st version dated September 29, containing a MIMIC section and more tables, and the corresponding Mplus inputs, data, and outputs here. The seven web tables correspond to tables 8, 10, 17, 18, 19, 20, and 21 of the first version. The new approach replaces parameter specifications of exact zeros with approximate zeros based on informative, small-variance priors.
It is argued that this produces an analysis that better rejects substantive theories. The proposed Bayesian approach is particularly beneficial in applications where parameters are added to a conventional model such that a non-identi ed model is obtained if maximum-likelihood estimation is applied. This approach is useful for measurement aspects of latent variable modeling such as with CFA and the measurement part of SEM.
Two application areas are studied, cross-loadings and residual correlations in CFA. The approach encompasses three elements: Model testing, model estimation, and model modi cation. Monte Carlo simulations and real data are analyzed using Mplus. Psychological Methods, Vol 17 3 , Sep , Responses to specific comments cover how to handle sign switching, nonconvergence and nonidentification, and prior choices in latent variable models.
Two new applications are included. The first one revisits the Kaplan science model by considering priors on primary parameters. The second one applies BSEM to the bifactor model that was hypothesized in the original Holzinger and Swineford study. Non-random dropout and the relative efficacy of escitalopram and nortriptyline in treating major depressive disorder.
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Journal of Psychiatric Research. Dropout rates differ between drugs, suggesting this assumption may not hold true. This paper examines the effect of non-random dropout on a comparison of two antidepressant drugs, escitalopram and nortriptyline, in the treatment of major depressive disorder. The GENDEP study followed adult patients with major depressive disorder over 12 weeks of treatment, and the primary analysis found no difference in efficacy of the two antidepressants under missing at random assumption.
Individuals who dropped out of the study were those who were not responding to treatment. Based on the best fitting NMAR model, it was found that escitalopram reduced symptom scores by an additional 1. We conclude that association between dropout and worsening symptoms led to an overestimate of the effectiveness of treatment, especially with nortriptyline, in the primary analysis. These findings review the primary analysis of GENDEP and suggest that, when non-random dropout is accounted for, escitalopram is more effective than nortriptyline in reducing symptoms of major depression.
Poisson growth mixture modeling of intensive longitudinal data: An application to smoking cessation behavior. Mixture factor analysis for approximating a nonnormally distributed continuous latent factor with continuous and dichotomous observed variables. A simulation study compares mixture factor analysis with normal maximum likelihood ML latent factor modeling. Different results emerge for continuous versus dichotomous outcomes.
For continuous outcome variables, both methods produce factor loading estimates with minimal bias regardless of latent factor skew, but the mixture factor analysis is more efficient. The method is demonstrated using data motivated by a study on youth with cystic fibrosis examining predictors of treatment adherence. Bayesian evaluation of inequality-constrained hypotheses in SEM models using Mplus. Structural Equation Modeling, 19, Using Bayesian priors for more flexible latent class analysis.
Click here to view Mplus inputs, data, and outputs used in this paper. We explore a new Bayesian approach that relaxes this assumption to an assumption of approximate independence. Instead of using a correlation matrix with correlations fixed to zero we use a correlation matrix where all correlations are estimated using an informative prior with mean zero but non-zero variance.
This more flexible approach easily accommodates LCA model misspecifications and thus avoids spurious class formations that are caused by the conditional independence violations. Simulation studies and real data analysis are conducted using Mplus. Item response modeling of forced-choice questionnaires. However, if scored with classical methodology, these questionnaires produce ipsative data, which lead to distorted scale relationships and make comparisons between individuals problematic. This research demonstrates how item response theory IRT modeling may be applied to overcome these problems.
Thurstonian IRT models are normal ogive models with structured factor loadings, structured uniquenesses, and structured local dependencies. These models can be straightforwardly estimated using structural equation modeling SEM software Mplus. A number of simulation studies are performed to investigate how latent traits are recovered under various forced-choice designs and provide guidelines for optimal questionnaire design. An empirical application is given to illustrate how the model may be applied in practice. It is concluded that when the recommended design guidelines are met, scores estimated from forced-choice questionnaires with the proposed methodology reproduce the latent traits well.
Missing not at random models for latent growth curve analyses. Psychological Methods, 16, Although MAR is often reasonable, there are situations where this assumption is unlikely to hold, leading to biased parameter estimates. One such example is a longitudinal study of substance use where participants with the highest frequency of use also have the highest likelihood of attrition, even after controlling for other correlates of missingness.
There is a large body of literature on missing not at random MNAR analysis models for longitudinal data, particularly in the field of biostatistics. Because these methods allow for a relationship between the outcome variable and the propensity for missing data, they require a weaker assumption about the missing data mechanism. This article describes 2 classic MNAR modeling approaches for longitudinal data: the selection model and the pattern mixture model. To date, these models have been slow to migrate to the social sciences, in part because they required complicated custom computer programs.
These models are now quite easy to estimate in popular structural equation modeling programs, particularly Mplus.
The purpose of this article is to describe these MNAR modeling frameworks and to illustrate their application on a real data set. Despite their potential advantages, MNAR-based analyses are not without problems and also rely on untestable assumptions. This article offers practical advice for implementing and choosing among different longitudinal models.
Conducting confirmatory latent class analysis using Mplus. Structural Equation Modeling, 18, LCA is most commonly used in an exploratory fashion whereby no parameters are specified a priori. Although this exploratory approach is reasonable when very little prior research has been conducted in the area under study, it can be very limiting when much is already known about the variables and population.
Confirmatory latent class analysis CLCA provides researchers with a tool for modeling and testing specific hypotheses about response patterns in the observed variables. CLCA is based on placing specific constraints on the parameters to reflect these hypotheses. The popular and easy-to-use latent variable modeling software packageMplus can be used to conduct a variety of CLCA types using these parameter constraints. This article focuses on the basic principles underlying the use of CLCA, and the Mplus programming code necessary for carrying it out.
Trajectories of depression severity in clinical trials of Duloxetine. Arch Gen Psychiatry, 68 12 : Objective: To assess whether growth mixture modeling can provide insights into antidepressant and placebo responses in clinical trials of patients with major depression. We analyzed the trajectories in the entire sample and then separately in all active arms and in all placebo arms. Effects of duloxetine hydrochloride, selective serotonin reuptake inhibitor SSRI , and covariates on the probability of following a particular trajectory were assessed.
Outcomes in different trajectories were compared using mixed-effects models. Patients: A total of patients with major depression.
Research with Diverse Groups: Research Designs and Multivariate Latent Modeling for Equivalence
Results: In the entire sample and in the antidepressanttreated subsample, we identified trajectories of responders However, placebo-treated patients were characterized by a single response trajectory. Duloxetine and SSRI did not differ in efficacy, and compared with placebo they significantly decreased the odds of following the nonresponder trajectory.
Antidepressant responders had significantly better HAM-D scores over time than placebo-treated patients, but antidepressant nonresponders had significantly worse HAM-D scores over time than the placebo-treated patients. Conclusions: Most patients treated with serotonergic antidepressants showed a clinical trajectory over time that is superior to that of placebo-treated patients. However, some patients receiving these medications did more poorly than patients receiving placebo. These data highlight the importance of ongoing monitoring of medication risks and benefits during serotonergic antidepressant treatment.
They should further stimulate the search for biomarkers or other predictors of responder status in guiding antidepressant treatment. International Journal of Geriatric Psychiatry. In Press. Inclusion of quadratic terms improved fit of the model -2 log likelihood difference: Identity statuses as developmental trajectories. A five-wave longitudinal study in early to middle and middle to late adolescents. Journal of Youth and Adolescence.
That is, we examined whether these statuses are distinct and relatively stable, over-time configurations of commitment strength, levels of in-depth exploration of present commitments, and consideration of alternative commitments.
The study examined identity development in a five-wave study of early-tomiddle Two kinds of moratorium were also found: the classical moratorium and searching moratorium. Females were more often in the advanced identity status trajectories, and stable differences were found between the trajectories in psychosocial adjustment. Study findings highlight that identity formation should be conceptualized as an over-time process. Personality types in adolescence: Change and stability and links with adjustment and relationships: A five-wave longitudinal study in early-to-middle and middle-to-late adolescence.
In Study 1, systematic evidence for personality change was found, in that the number of overcontrollers and undercontrollers decreased, whereas the number of resilients increased. Undercontrol, in particular, was found to peak in early-to-middle adolescence. We also found substantial stability of personality types, because Personality change was mainly characterized by 2 transitions: overcontrol 3 resiliency and undercontrol 3 resiliency.
The transitional analyses implied that the resilient type serves more often as the end point of personality development in adolescence than do overcontrol and undercontrol. Analyses of the personality type trajectories also revealed that the majority of adolescents who change personality type across 5 years made only 1 transition.
Study 2 revealed systematic differences between resilients and overcontrollers in anxiety. Stable resilients were less anxious over time than were stable overcontrollers. Further, change from overcontrol to the resilient type was accompanied by decreases in anxiety, whereas change from the resilient type to overcontrol was accompanied by an increase in anxiety.
Similarly, systematic differences between personality types were found in the formation of intimate relationships. Mplus inputs used in this paper can be downloaded here.
First, no study provided evidence of the factorial equivalence of this instrument across samples of depressive and community participants. This is intriguing regarding that the CES-D was specifically designed to identify clinical depression in epidemiological community adults. Second, only one study relied on systematic tests of measurement invariance as implemented within confirmatory factor analyses CFA and this study did not consider the higher order depression structure, although it is the CES-D global scale score that is most often used in the context of epidemiological studies.
It thus remains unknown whether the commonly recognized gender differences in depression could be related or not to measurement biases. Third, few studies investigated the screening properties of the CES-D in non-English samples and their results have been inconsistent. Finally, very few studies took into account the ordered-categorical nature of the CES-D answer scale. The purpose of this study was thus to examine the construct validity i.
Methods: A total sample of participants, comprising clinically depressed patients and community adults, was involved in this study. The factorial validity and the measurement and latent mean invariance of the CES-D, across gender and clinical status, were verified through CFAs based on ordered-categorical items. Correlation and receiver operator characteristic curves were also used to test the convergent validity and screening properties of the CES-D. Conclusion: This instrument may be useful for the assessment of depressive symptoms or for the screening depressive disorders in the context of epidemiological studies targeting French patients and community men and women with a background similar to those from the present study.
Applications of causally defined direct and indirect effects in mediation analysis using SEM in Mplus. Click here to view the Technical appendix that goes with this paper and click here for the Mplus input appendix. It presents causally-defined direct and indirect effects for continuous, binary, ordinal, nominal, and count variables.
The expansion to non-continuous mediators and outcomes offers a broader array of causal mediation analyses than previously considered in SEM practice. A new result is the ability to handle mediation by a nominal variable. Examples with a binary outcome and a binary, ordinal and nominal mediator are given, using Mplus to compute the effects. The causal effects require strong assumptions even in randomized designs, especially sequential ignorability, which is presumably often violated to some extent due to mediator-outcome confounding.
To study the effects of violating this assumption, it is shown how a sensitivity analysis can be carried out using Mplus. This can be used both in planning a new study and in evaluating the results of an existing study. Beyond multilevel regression modeling: Multilevel analysis in a general latent variable framework. Roberts eds , Handbook of Advanced Multilevel Analysis, pp. New York: Taylor and Francis. Multilevel modeling, however, is relevant for nested data not only with regression and growth analysis but with all types of statistical analyses.
This chapter has two aims. First, it shows that already in the traditional multilevel analysis areas of regression and growth there are several new modeling opportunities that should be considered. Second, it gives an overview with examples of multilevel modeling for path analysis, factor analysis, structural equation modeling, and growth mixture modeling. Examples include two extensions of two-level regression analysis with measurement error in the level 2 covariate and a level 1 mixture; two-level path analysis and structural equation modeling; two-level exploratory factor analysis of classroom misbehavior; two-level growth modeling using a two-part model for heavy drinking development; an unconventional approach to three-level growth modeling of math achievement; and multilevel latent class mediation of high school dropout using multilevel growth mixture modeling of math achievement development.
Click here to view Mplus outputs used in this paper. Both existing and new models are explored for pattern-mixture and selection type modeling. The trajectory class analysis provides a new way to assess drug efficiency. Software is available for sensitivity analysis using the extensive set of missing data models available in the general latent variable framework.
General approaches to analysis of course: Applying growth mixture modeling to randomized trials of depression medication. Shrout ed. New York: Oxford University Press. The motivation is a study of depression medication in a double-blind placebo-controlled trial. Studies of this type typically show placebo response and placebo non response. Growth mixture modeling GMM is well suited for representing such heterogeneity among subjects in that it can identify di erent types of trajectory shapes. GMM can be seen as a combination of conventional mixed effects modeling and cluster analysis, also allowing prediction of class membership and estimation of each individual's most likely class membership.
GMM has particularly strong potential for analyses of randomized trials because it responds to the need to investigate for whom a treatment is eff ective by allowing for di erent treatment e ects in di erent trajectory classes. In this trial, a separate analysis of the placebo group nds evidence of a placebo response trajectory class with a strong initial improvement, followed by a later worsening.
A separate analysis of the medication group shows two types of responder classes, one with an initial improvement only and one with a sustained improvement. A joint analysis of the placebo and medication groups makes it possible to estimate medication e ects in the presence of placebo-response effects and shows bene ts of medication. Analysis strategies and alternatives for assessing medication e ects are discussed. Key words: Randomized trials, growth modeling, causal e ects, latent variables, trajectory classes, maximum likelihood. Sample size and power estimates for a confirmatory factor analytic model in exercise and sport: A Monte Carlo approach.
The purpose of using Monte Carlo methods in a validity study is to improve the methodological approach within a study where the primary focus is on construct validity issues and not on advancing statistical theory. The purpose of this study is to demonstrate how Monte Carlo methods can be used to determine sample size and to estimate power for a confirmatory factor analytic model under model-data conditions commonly encountered in exercise and sport. Technical terms e. Accepted for publication in Prevention Science. Both the classroom-centered and family-centered interventions were designed to reduce the risk for later conduct problems by enhancing the child behavior management practices of teachers and parents, respectively.
We first modeled growth trajectories in each of the two time periods with separate GMMs. Subsequently, we tested whether the interventions had direct effects on trajectory class membership in grades and For males, both the classroom-centered and family-centered interventions had significant direct effects on trajectory class membership in grades , whereas only the classroom-centered intervention had a significant effect on class membership in grades Significant direct effects for females were confined to grades for the classroom-centered intervention.
Further analyses revealed that both the classroom-centered and family-centered intervention males were significantly more likely than control males to transition from the high trajectory class in grades to a low class in grades Effects for females in classroom-centered interventions went in the hypothesized direction but did not reach significance. Growth mixture models in longitudinal research. Community Psychol. Concepts, issues and applications, 2nd edn.
Recent methodological and statistical extension are focused on the consideration of unobserved heterogeneity in empirical data. The paper discusses applications of growth mixture models with data on delinquent behavior of adolescents from the German panel study Crime in the modern City CrimoC Boers et al.
Observed as well as unobserved heterogeneity will be considered with growth mixture models. Special attention is given to the distribution of the outcome variables as counts. Poisson and negative binomial distributions with zero inflation are considered in the proposed growth mixture models variables.
Different model specifications will be emphasized with respect to their particular parameterizations. Latent variable mixture models: A promising approach for the validation of patient reported outcomes. Quality of Life Research. The related assumption of sample homogeneity has been assessed in various ways, including the many approaches to differential item functioning analysis.
Methods This expository paper describes the use of latent variable mixture modeling LVMM , in conjunction with item response theory IRT , to examine: a whether a sample is homogeneous with respect to a unidimensional measurement model, b implications of sample heterogeneity with respect to model-predicted scores theta , and c sources of sample heterogeneity.
Results The sample was not homogeneous with respect to a unidimensional measurement structure. Specification of three latent classes, to account for sample heterogeneity, resulted in significantly improved model fit. The latent classes were partially explained by demographic and health-related variables. Conclusion The illustrative analyses demonstrate the value of LVMM in revealing the potential implications of sample heterogeneity in the measurement of PROs.
Current methodological considerations in exploratory and confirmatory factor analysis. Journal of Psychoeducational Assessment, 29, They must decide on an appropriate sample size to achieve accurate parameter estimates and adequate power, a factor model and estimation method, a method for determining the number of factors and evaluating model fit, and a rotation criterion.
Unfortunately, researchers continue to use outdated methods in each of these areas. The present article provides a current overview of these areas in an effort to provide researchers with up-to-date methods and considerations in both exploratory and confirmatory factor analysis. A demonstration was provided to illustrate current approaches.
Choosing between confirmatory and exploratory methods is also discussed, as researchers often make incorrect assumptions about the application of each. J,, Drotar, S. Addressing the problem of switched class labels in latent variable mixture model simulation studies. Prior to a mixture analysis it is useful to investigate model performance in a simulation study that reflects the research settings. Multiple data sets are generated under 1 or more models, and alternative models are fitted to the data. The aggregation of results over multiple data sets is complicated by the fact that mixture models are only identified up to a permutation of the class labels.
Estimated class labels are arbitrary, with the effect that the estimated parameters for Class 1 could be incorrectly labeled as Class 2, Class 3, and so forth, relative to their data generating labels. In a simulation study, the detection of switched labels needs to be automated. Switched class labels are not necessarily simple to detect.
This article describes different possible scenarios of switched class labels, and develops an algorithm implemented in R that a detects switched labels, and b provides information that can be used to either correct class labels or to discard a particular data set from a simulation if class labels are ambivalent. The algorithm is useful in Monte Carlo simulations involving latent variable mixture models.
Walton, K. The dimensional nature of externalizing behaviors in adolescence: Evidence from a direct comparison of categorical, dimensional, and hybrid models. Forthcoming in Journal of Ab Child Psych. Forthcoming in Journal of Abnormal Child Psychology. Newer statistical technologies now allow categorical and dimensional models of psychopathology to be compared empirically. In this study, we directly compared the fit of categorical and dimensional models of externalizing behaviors in a large and representative community sample of adolescents at two time points separated by nearly 2.
Delinquent and aggressive behaviors were assessed with child and parent Child Behavior Checklist reports. Latent trait, latent class, and factor mixture models were fit to the data, and at both time points, the latent trait model provided the best fit to the data. The item parameters were inspected and interpreted, and it was determined that the items were differentially sensitive across all regions of the dimension. We conclude that classification models can be based on empirical evidence rather than a priori preferences, and while current classification systems conceptualize externalizing problems in terms of discrete groups, they can be better conceptualized as dimensions.
Bayesian analysis of latent variable models using Mplus. Version 4. Bayesian analysis using Mplus: Technical implementation. Multiple imputation with Mplus. Plausible values for latent variables using Mplus. A multigroup structural equation approach: A demonstration by testing variation of firm profitability across EU samples.
The proposed methods are applied to analyze an accounting profitability database covering more than , firms in the 15 European Union EU countries in the period to A multivariate model with permanent and dynamic latent components of profitability is used to assess across-country variation of firm level profitability and persistence. We show that there are substantial differences among these countries, despite the partial integration of their economies. Estimation of supplementary parameters are proposed as a way to characterize persistence in each country, as well as across-group variation of model parameters.
This methodology is more widely applicable in international organizational research. Latent transition analysis with a mixture item response theory measurement model. Unlike the LTA, which was developed with a latent class measurement model, the LTA-MRM permits within-class variability on the latent variable, making it more useful for measuring treatment effects within latent classes.
A real data application of a mathematics intervention with middle school students indicated that the LTA-MRM clearly detected the intervention effect and also provided a means of helping to better understand the effects compared to a standard multiwave analysis of variance. Mixture modeling with behavioral data. Doctoral dissertation, University of California, Los Angeles.
There is a need for innovate statistical methods to analyze data to which will help inform the development of new strategies to deal with the issues associated with behavioral problems. The three papers in this dissertation focus on explicating certain mixture models which have shown promise in analyzing behavioral data. In addition, most observable variables are affected by method variance, with the results obtained using a method Show page numbers Download PDF. Search form icon-arrow-top icon-arrow-top. Page Site Advanced 7 of Edited by: Neil J.
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Related Research with Diverse Groups: Research Designs and Multivariate Latent Modeling for Equivalence
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