{"title":"The Influence of Misspecification of the Heteroscedasticity on Multilevel Regression Parameter and Standard Error Estimates","authors":"E. Korendijk, C. Maas, M. Moerbeek, P. Heijden","doi":"10.1027/1614-2241.4.2.67","DOIUrl":"https://doi.org/10.1027/1614-2241.4.2.67","url":null,"abstract":"Like in ordinary regression models, in multilevel analysis, homoscedasticity of the residual variances is an assumption that is mostly unchecked. However, in experimental research, the residual variance component at level two may differ in the experimental and the control condition, leading to heteroscedastic second level variances. Using a simulation study, the consequences of ignoring second level heteroscedasticity on the estimation of the fixed and random parameters and their standard errors was investigated. It was found that the standard error of the second level variance is underestimated, but that the estimated fixed parameters of the independent variables, the first level variance and their standard errors are mostly unbiased.","PeriodicalId":18476,"journal":{"name":"Methodology: European Journal of Research Methods for The Behavioral and Social Sciences","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2008-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57292453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Kelava, H. Moosbrugger, Polina Dimitruk, K. Schermelleh-engel
{"title":"Multicollinearity and missing constraints: A comparison of three approaches for the analysis of latent nonlinear effects.","authors":"A. Kelava, H. Moosbrugger, Polina Dimitruk, K. Schermelleh-engel","doi":"10.1027/1614-2241.4.2.51","DOIUrl":"https://doi.org/10.1027/1614-2241.4.2.51","url":null,"abstract":"Multicollinearity complicates the simultaneous estimation of interaction and quadratic effects in structural equation modeling (SEM). So far, approaches developed within the Kenny-Judd (1984) tradition have failed to specify additional and necessary constraints on the measurement error covariances of the nonlinear indicators. Given that the constraints comprise, in part, latent linear predictor correlations, multicollinearity poses a problem for such approaches. Klein and Moosbrugger’s (2000) latent moderated structural equations approach (LMS) approach does not utilize nonlinear indicators and should therefore not be affected by this problem. In the context of a simulation study, we varied predictor correlation and the number of nonlinear effects in order to compare the performance of three approaches developed for the estimation of simultaneous nonlinear effects: Ping’s (1996) two-step approach, a correctly extended Joreskog-Yang (1996) approach, and LMS. Results show that in contrast to the Joreskog-Ya...","PeriodicalId":18476,"journal":{"name":"Methodology: European Journal of Research Methods for The Behavioral and Social Sciences","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2008-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57292420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Effect of the Number of Response Categories on the Reliability and Validity of Rating Scales","authors":"Luis M. Lozano, E. García-Cueto, J. Muñiz","doi":"10.1027/1614-2241.4.2.73","DOIUrl":"https://doi.org/10.1027/1614-2241.4.2.73","url":null,"abstract":"The Likert-type format is one of the most widely used in all types of scales in the field of social sciences. Nevertheless, there is no definitive agreement on the number of response categories that optimizes the psychometric properties of the scales. The aim of the present work is to determine in a systematic fashion the number of response alternatives that maximizes the fundamental psychometric properties of a scale: reliability and validity. The study is carried out with data simulated using the Monte Carlo method. We simulate responses to 30 items with correlations between them ranging from 0.2 to 0.9. We also manipulate sample size, analyzing four different sizes: 50, 100, 200, and 500 cases. The number of response options employed ranges from two to nine. The results show that as the number of response alternatives increases, both reliability and validity improve. The optimum number of alternatives is between four and seven. With fewer than four alternatives the reliability and validity decrease, an...","PeriodicalId":18476,"journal":{"name":"Methodology: European Journal of Research Methods for The Behavioral and Social Sciences","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2008-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1027/1614-2241.4.2.73","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57292472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Longitudinal Data Analysis with Structural Equations","authors":"J. Rosel, I. Plewis","doi":"10.1027/1614-2241.4.1.37","DOIUrl":"https://doi.org/10.1027/1614-2241.4.1.37","url":null,"abstract":"Abstract. In this paper we review different structural equation models for the analysis of longitudinal data: (a) univariate models of observable variables, (b) multivariate models of observable variables, (c) models with latent variables, (d) models that are unconditioned or conditioned to other variables (depending on the variability of the independent variables: time-varying or time-invariant, and depending on the type of independent variables: of latent variables or of observable variables), (e) models with interaction of variables, (f) models with nonlinear variables, (g) models with a constant, (h) with single level and multilevel measurement, and (i) other advances in SEM of longitudinal data (latent growth curve model, latent difference score, etc.). We pay more attention to the interaction of variables and to nonlinear transformations of variables because they are not frequently used in empirical investigation. They do, however, offer interesting possibilities to researchers who wish to verify re...","PeriodicalId":18476,"journal":{"name":"Methodology: European Journal of Research Methods for The Behavioral and Social Sciences","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2008-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1027/1614-2241.4.1.37","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57292400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Factorial Invariance and The Specification of Second-Order Latent Growth Models.","authors":"Emilio Ferrer, Nekane Balluerka, Keith F Widaman","doi":"10.1027/1614-2241.4.1.22","DOIUrl":"https://doi.org/10.1027/1614-2241.4.1.22","url":null,"abstract":"Latent growth modeling has been a topic of intense interest during the past two decades. Most theoretical and applied work has employed first-order growth models, in which a single manifest variable serves as indicator of trait level at each time of measurement. In the current paper, we concentrate on issues regarding second-order growth models, which have multiple indicators at each time of measurement. With multiple indicators, tests of factorial invariance of parameters across times of measurement can be tested. We conduct such tests using two sets of data, which differ in the extent to which factorial invariance holds, and evaluate longitudinal confirmatory factor, latent growth curve, and latent difference score models. We demonstrate that, if factorial invariance fails to hold, choice of indicator used to identify the latent variable can have substantial influences on the characterization of patterns of growth, strong enough to alter conclusions about growth. We also discuss matters related to the scaling of growth factors and conclude with recommendations for practice and for future research.","PeriodicalId":18476,"journal":{"name":"Methodology: European Journal of Research Methods for The Behavioral and Social Sciences","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1027/1614-2241.4.1.22","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"28624901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Model error in covariance structure models: Some implications for power and Type I error.","authors":"Donna L Coffman","doi":"10.1027/1614-2241.4.4.159","DOIUrl":"https://doi.org/10.1027/1614-2241.4.4.159","url":null,"abstract":"<p><p>The present study investigated the degree to which violation of the parameter drift assumption affects the Type I error rate for the test of close fit and power analysis procedures proposed by MacCallum, Browne, and Sugawara (1996) for both the test of close fit and the test of exact fit. The parameter drift assumption states that as sample size increases both sampling error and model error (i.e. the degree to which the model is an approximation in the population) decrease. Model error was introduced using a procedure proposed by Cudeck and Browne (1992). The empirical power for both the test of close fit, in which the null hypothesis specifies that the Root Mean Square Error of Approximation (RMSEA) ≤ .05, and the test of exact fit, in which the null hypothesis specifies that RMSEA = 0, is compared with the theoretical power computed using the MacCallum et al. (1996) procedure. The empirical power and theoretical power for both the test of close fit and the test of exact fit are nearly identical under violations of the assumption. The results also indicated that the test of close fit maintains the nominal Type I error rate under violations of the assumption.</p>","PeriodicalId":18476,"journal":{"name":"Methodology: European Journal of Research Methods for The Behavioral and Social Sciences","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1027/1614-2241.4.4.159","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"29681071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Polina Dimitruk, K. Schermelleh-engel, A. Kelava, H. Moosbrugger
{"title":"Challenges in Nonlinear Structural Equation Modeling","authors":"Polina Dimitruk, K. Schermelleh-engel, A. Kelava, H. Moosbrugger","doi":"10.1027/1614-2241.3.3.100","DOIUrl":"https://doi.org/10.1027/1614-2241.3.3.100","url":null,"abstract":"Abstract. Challenges in evaluating nonlinear effects in multiple regression analyses include reliability, validity, multicollinearity, and dichotomization of continuous variables. While reliability and validity issues are solved by employing nonlinear structural equation modeling, multicollinearity remains a problem which may even be aggravated when using latent variable approaches. Further challenges of nonlinear latent analyses comprise the distribution of latent product terms, a problem especially relevant for approaches using maximum likelihood estimation methods based on multivariate normally distributed variables, and unbiased estimates of nonlinear effects under multicollinearity. The only methods that explicitly take the nonnormality of nonlinear latent models into account are latent moderated structural equations (LMS) and quasi-maximum likelihood (QML). In a small simulation study both methods yielded unbiased parameter estimates and correct estimates of standard errors for inferential statistic...","PeriodicalId":18476,"journal":{"name":"Methodology: European Journal of Research Methods for The Behavioral and Social Sciences","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2007-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1027/1614-2241.3.3.100","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57292354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Visualizing Multivariate Dependencies with Association Chain Graphs","authors":"M. Höfler, T. Brückl, A. Bittner, R. Lieb","doi":"10.1027/1614-2241.3.1.24","DOIUrl":"https://doi.org/10.1027/1614-2241.3.1.24","url":null,"abstract":"In a recent paper, a new type of graph to visualize the results from graphical models was proposed. Association chain graphs (ACGs) provide a richer visualization than conventional graphs (directed acyclic and recursive regression graphs) if the data can be described with only a small number of parameters. ACGs display not only which associations reach statistical significance, but also the magnitude of associations (confidence intervals for statistical main effects) as the contrast color to the background color of the graph. In this paper, the ACG visualization is extended especially for the case where all variables are binary by illustrating their relative frequencies. This shows the degrees of associations not only on the individual (as expressed by odds ratios or other indexes of association) but also on the community level. We applied the approach to an extensive example of birth and childhood factors for the onset of affective mental disorders using data from the EDSP (Early Developmental Stages of ...","PeriodicalId":18476,"journal":{"name":"Methodology: European Journal of Research Methods for The Behavioral and Social Sciences","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2007-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57292307","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Longitudinal Analysis of Adolescents Deviant and Delinquent Behavior: Applications of Latent Class","authors":"Jost Reinecke","doi":"10.1027/1614-2241.2.3.100","DOIUrl":"https://doi.org/10.1027/1614-2241.2.3.100","url":null,"abstract":"This article presents applications of different growth mixture models considering unobserved heterogeneity within the framework of Mplus (Muthen & Muthen, 2001a, 2001b, 2004). Latent class growth mixture models are discussed under special consideration of count variables that can be incorporated into the mixtures via the Poisson and the zero-inflated Poisson model. Fourwave panel data from a German criminological youth study (Boers et al., 2002) is used for the model analyses. Three classes can be obtained from the data: Adolescents with almost no deviant and delinquent activities, a medium proportion of adolescents with a low increase of delinquency, and a small number with a larger growth starting on a higher level. Considering the zero inflation of the data results in better model fits compared to the Poisson model only. Linear growth specifications are almost sufficient. The conditional application of the mixture models includes gender and educational level of the schools as time-independent predictor...","PeriodicalId":18476,"journal":{"name":"Methodology: European Journal of Research Methods for The Behavioral and Social Sciences","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2006-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57292239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
E. Davidov, Kajsa Yang-Hansen, J. Gustafsson, P. Schmidt, S. Bamberg
{"title":"Does Money Matter? A Theory-Driven Growth Mixture Model to Explain Travel-Mode Choice with Experimental Data","authors":"E. Davidov, Kajsa Yang-Hansen, J. Gustafsson, P. Schmidt, S. Bamberg","doi":"10.1027/1614-2241.2.3.124","DOIUrl":"https://doi.org/10.1027/1614-2241.2.3.124","url":null,"abstract":"In the present article we apply a growth mixture model using Mplus via STREAMS to delineate the mechanism underlying travel-mode choice. Three waves of an experimental field study conducted in Frankfurt Main, Germany, are applied for the statistical analysis. Five major questions are addressed: (1) whether the choice of public transport rather than the car changes over time; (2) whether a soft policy intervention to change travel mode choice has any effect on the travel-mode chosen; (3) whether one can identify different groups of people regarding the importance allocated to monetary and time considerations for the decision of which travel mode to use; (4) whether the different subgroups of people have different initial states and rates of change in their travel-model choices; (5) whether sociodemographic variables have an additional effect on the latent class variables and on the changes in travel-mode choice over time. We also found that choice of public transportation in our study is stable over time. ...","PeriodicalId":18476,"journal":{"name":"Methodology: European Journal of Research Methods for The Behavioral and Social Sciences","volume":null,"pages":null},"PeriodicalIF":3.1,"publicationDate":"2006-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"57292250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}