Helfried Moosbrugger

Maximum likelihood estimation of latent interaction effects with the LMS method

In the context of structural equation modeling, a general interaction model with multiple latent interaction effects is introduced. A stochastic analysis represents the nonnormal distribution of the joint indicator vector as a finite mixture of normal distributions. The Latent Moderated Structural Equations (LMS) approach is a new method developed for the analysis of the general interaction model that utilizes the mixture distribution and provides a ML estimation of model parameters by adapting the EM algorithm. The finite sample properties and the robustness of LMS are discussed. Finally, the applicability of the new method is illustrated by an empirical example.

Advanced nonlinear latent variable modeling: Distribution analytic LMS and QML estimators of interaction and quadratic effects

Interaction and quadratic effects in latent variable models have to date only rarely been tested in practice. Traditional product indicator approaches need to create product indicators (e.g., x 1 2, x 1 x 4) to serve as indicators of each nonlinear latent construct. These approaches require the use of complex nonlinear constraints and additional model specifications and do not directly address the nonnormal distribution of the product terms. In contrast, recently developed, easy-to-use distribution analytic approaches do not use product indicators, but rather directly model the nonlinear multivariate distribution of the measured indicators. This article outlines the theoretical properties of the distribution analytic Latent Moderated Structural Equations (LMS; Klein & Moosbrugger, 2000) and Quasi-Maximum Likelihood (QML; Klein & Muthén, 2007) estimators. It compares the properties of LMS and QML to those of the product indicator approaches. A small simulation study compares the two approaches and illustrates the advantages of the distribution analytic approaches as multicollinearity increases, particularly in complex models with multiple nonlinear terms. An empirical example from the field of work stress applies LMS and QML to a model with an interaction and 2 quadratic effects. Example syntax for the analyses with both approaches is provided.

Challenges in Nonlinear Structural Equation Modeling

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...

The use of virtual environments based on a modification of the computer game Quake III Arena ® in psychological experimenting

We investigated whether newly developed virtual 3D environments (VEs) based on a modification of the computer game Quake III Arena^(R) are suitable for psychological experimenting. Internal validity of data collected in VEs may be threatened due to a priori individual differences in general performance in VE navigation and in susceptibility to cybersickness. The main question was whether individual differences in performance can be diminished by means of training. Additionally, the susceptibility of different subsamples to cybersickness when moving within VEs was examined. 85 participants took part in an experiment where they had to fulfill simple tasks in three VEs. Navigation performance was measured as the time participants needed to make their way through the VEs. Differences in navigation performance between different levels of experience were diminished by training, indicating that internal validity can be obtained. A classification tree reveals that game-inexperienced female participants aged over 31 years have the highest risk of experiencing cybersickness. VEs based on modifications of computer games seem to be an extremely promising and inexpensive possibility for the administration of psychological experiments.

Cross-sectional and longitudinal confirmatory factor models for the German Test Anxiety Inventory: A construct validation

Construct validity of the German Test Anxiety Inventory (TAI-G) was tested in two respects. Firstly, the purported four-dimensional structure of the TAI-G (comprising subscales Emotionality, Worry, Interference, and Lack of Confidence) as well as relations of the test anxiety dimensions to self-efficacy were tested. Secondly, the trait conception of the TAI-G was tested within the framework of Latent State-Trait theory. The TAI-G was given to a student sample (N=302) on three occasions with a time interval of 2 weeks along with a study-specific self-efficacy scale on occasion 1. Dimensionality assumptions as well as relations with self-efficacy were tested using cross-sectional second-order confirmatory factor analysis. The trait conception was tested separately for TAI-G subscales by specifying longitudinal confirmatory factor models (Latent State-Trait models) and by calculating variance proportions of manifest variables (Latent State-Trait coefficients) referring to different sources of systematic variance (person, situation, and method) based on parameter estimates of the models. Results were supportive of both the purported four-dimensional structure and hypothesized relationships to self-efficacy (i.e., acceptable model fit) as well as of the trait conception of test anxiety (i.e., acceptable model fit and high proportion of variance due to person component). Implications for further validation studies were discussed.

Decomposing Person and Occasion-Specific Effects: An Extension of Latent State-Trait (LST) Theory to Hierarchical LST Models.

An extension of latent state-trait (LST) theory to hierarchical LST models is presented. In hierarchical LST models, the covariances between 2 or more latent traits are explained by a general 3rd-order factor, and the covariances between latent state residuals pertaining to different traits measured on the same measurement occasion are explained by 2nd-order latent occasion-specific factors. Analogous to recent developments in multitrait-multimethod methodology, all factors are interpreted in relation to factors taken as comparison standards. An empirical example from test anxiety research illustrates how estimates of additive variance components due to general trait, specific trait, occasion, state residual, method, and measurement error can be obtained using confirmatory factor analysis. Advantages and limitations of these models are discussed.

Multicollinearity and Missing Constraints

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...

Exploratorische (EFA) und Konfirmatorische Faktorenanalyse (CFA)

Zur Konstruktvalidierung eines neu entwickelten Fragebogens oder Tests wird haufig entweder die exploratorische Faktorenanalyse oder die konfirmatorische Faktorenanalyse eingesetzt, um zu uberprufen, ob die Items hoch mit den Faktoren (Konstrukten, Dimensionen, Merkmalen) korrelieren, die mit Hilfe der Items gemessen werden sollen.

A Confirmatory Analysis of Item Reliability Trends (CAIRT): Differentiating True Score and Error Variance in the Analysis of Item Context Effects.

Numerous studies have shown increasing item reliabilities as an effect of the item position in personality scales. Traditionally, these context effects are analyzed based on item-total correlations. This approach neglects that trends in item reliabilities can be caused either by an increase in true score variance or by a decrease in error variance. This article presents the Confirmatory Analysis of Item Reliability Trends (CAIRT) that allows estimating both trends separately within a structural equation modeling framework. Results of a simulation study prove the CAIRT method to provide reliable and independent parameter estimates; the power exceeds the analysis of item-total correlations. We present an empirical application to self- and peer ratings collected in an Internet-based experiment. Results show that reliability trends are caused by increasing true score variance in self-ratings and by decreasing error variance in peer ratings.

Die “ARES-Skalen” zur Erfassung der individuellen BIS- und BAS-Sensitivität

Zusammenfassung: Das psychobiologische Modell von J.A. Gray nimmt zwei grundlegende Emotionssysteme als Basis zweier korrespondierender grundlegender Personlichkeitsdimensionen an: Das Behavioral Inhibition System (BIS) und das Behavioral Approach System (BAS). Zur Erfassung der Dimensionen BIS- und BAS-Sensitivitat stellen die BIS/BAS-Skalen von Carver und White (1994) die bisher viel versprechendste Skalenkonstruktion dar, jedoch sind diese hinsichtlich der Skaleneigenschaften noch nicht vollig zufrieden stellend. Aufbauend auf dem Grayschen Modell und unter Ruckgriff auf zentrale Uberlegungen von Carver und White wurden deutsche Skalen zur Erfassung der Sensitivitat der beiden Emotionssysteme (Action Regulating Emotion Systems; ARES) in einer Langfassung (58 Items) und einer Kurzfassung (20 Items) neu konstruiert. Die ARES-Skalen enthalten die Subskalen BIS I “Angstlichkeit” und BIS II “Frustration” zur Erfassung der individuellen BIS- und die Subskalen BAS I “Antrieb” und BAS II “Freude” zur Erfassung...