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Repeated measures data are widely used in social and behavioral sciences, e.g., to investigate the trajectory of an underlying phenomenon over time. A variety of different mixed-effects models, a type of statistical modeling approach for repeated measures data, have been proposed and they differ mainly in two aspects: (1) the distributional assumption of the dependent variable and (2) the linearity of the model. Distinct combinations of these characteristics encompass a variety of modeling techniques. Although these models have been independently discussed in the literature, the most flexible framework -- the generalized nonlinear mixed-effects model (GNLMEM) -- can be used as a modeling umbrella to encompass these modeling options for repeated measures data. Therefore, the aim of this paper is to explicate on the different mixed-effects modeling techniques guided by the distributional assumption and model linearity choices using the GNLMEM as a general framework. Additionally, empirical examples are used to illustrate the versatility of this framework.

Understanding students' readiness for precalculus and calculus at the community college level is critical not only because of the key role community colleges play in higher education but also because calculus remains a gateway course for students in advancing to higher level mathematics. The Algebra and Precalculus Concept Readiness Assessment for Community Colleges (APCR-CC) was designed to investigate community college students' quantitative reasoning abilities and conceptual understanding in algebra. The present study investigates the psychometric properties of the APCR-CC instrument using item response theory based on a sample of intermediate and college algebra students from six community colleges collected in a pretest (N = 1,131) and posttest (N = 772) setting. We examine unidimensionality, item fit, local item independence, measurement invariance, and sensitivity to instruction. Our findings suggest that the APCR-CC instrument is sufficiently characterized by one underlying construct, local dependence does not seem to be an issue, and 80% of the items in the APCR-CC instrument are sensitive to instruction.

Background: Empirical evidence regarding the development of sensory responsivity in young children at high likelihood to develop autism spectrum disorder (ASD) remains relatively limited. It is unclear how sensory responsivity behaviors may change over time and impact later developmental outcomes. The goals of this study were to (a) characterize developmental trajectories of sensory responsivity across infancy (∼12 months), toddlerhood (∼24 months), and school age (6–11 years) in children at high and low familial likelihood for ASD; and (b) determine if sensory responsivity in infancy predicts adaptive and cognitive functioning at school age among children with ASD. Methods: Generalized linear mixed effects models were used to examine scores from the Sensory Experiences Questionnaire in three groups of children including high‐likelihood children later diagnosed with ASD (HL‐ASD; n = 30), high‐likelihood children without ASD (HL‐Neg; n = 150), and low‐likelihood control children not meeting ASD diagnostic criteria (LL‐Neg; n = 94). Hierarchical linear regression was then used to examine the association between sensory responsivity scores in infancy and functional adaptive and cognitive outcomes at school age for children at high likelihood of ASD. Results: Development of sensory responsivity from infancy to later childhood is best estimated by the effects of chronological age and Group for Sensory Seeking and Hypo responsivity and the additional effect of the interaction of Group and chronological age for Total and Hyper responsivity. Early elevated Hypo responsivity and Sensory Seeking scores are negatively associated with later adaptive behavior but not cognitive level. Conclusion: Overall, higher degrees of Sensory Seeking and Hypo sensory responsivity are detectable in autistic children's behavioral repertoires by 12 months of age and associate with reduced adaptive functioning in middle childhood. These results point to the potential importance of early detection and treatment implications of early sensory behaviors. [ABSTRACT FROM AUTHOR]

Piecewise mixed-effects models are useful for analyzing longitudinal educational and psychological data sets to model segmented change over time. These models offer an attractive alternative to commonly used quadratic and higher-order polynomial models because the coefficients obtained from fitting the model have meaningful substantive interpretation. The current study thus focuses on the estimation of piecewise mixed-effects model with unknown "random" change points using maximum likelihood (ML) as described in Du Toit and Cudeck (2009). Previous simulation work (Wang & McArdle, 2008) showed that Bayesian estimation produced reliable parameter estimates for the piecewise model in comparison to frequentist procedures (i.e., first-order Taylor expansion and the adaptive Gaussian quadrature) across all simulation conditions. In the current article a small Monte Carlo simulation study was conducted to assess the performance of the ML approach, a frequentist procedure, and the Bayesian approach for fitting linear--linear piecewise mixed-effects model. The obtained findings show that ML estimation approach produces reliable and accurate estimates under the conditions of "small" residual variance of the observed variables, and that the "size" of the residual variance had the most impact on the quality of model parameter estimates. Second, neither ML nor Bayesian estimation procedures performed well under all manipulated conditions with respect to the accuracy and precision of the estimated model parameters.

In this paper, we examine the relationships between teachers' subject matter preparation and experience in teaching and their performance on an instrument measuring mathematical knowledge for teaching Algebra 1. We administered the same instrument to two different samples of teachers−high school practicing teachers and community college faculty − who teach the same algebra content in different levels of institutions, and we compared the performance of the two different samples and the relationships between the measured knowledge and their educational and teaching background across the samples. The comparison suggested that the community college faculty possess a higher level of mathematical knowledge for teaching Algebra 1 than high school teachers. The subsequent analyses using the Multiple Indicator Multiple Causes (MIMIC) models based on our hypothesis on the factors contributing to the differences in the knowledge between the two teacher samples suggest that experience teaching advanced algebra courses has positive effects on the mathematical knowledge for teaching Algebra 1 in both groups. Highlighting the positive effect of algebra-based teaching experience on test performance, we discuss the implications of the impact of subject specific experience in teaching on teachers' mathematical content knowledge for teaching. [ABSTRACT FROM AUTHOR]

Objective: Accurate estimation of developmental trajectories can inform instruction and intervention. We compared the fit of linear, quadratic, and piecewise mixed-effects models of reading development among students with learning disabilities relative to their typically developing peers. Method: We drew an analytic sample of 1,990 students from the nationally representative Early Childhood Longitudinal Study--Kindergarten Cohort of 1998, using reading achievement scores from kindergarten through eighth grade to estimate three models of students' reading growth. Results: The piecewise mixed-effects models provided the best functional form of the students' reading trajectories as indicated by model fit indices. Results showed slightly different trajectories between students with learning disabilities and without disabilities, with varying but divergent rates of growth throughout elementary grades, as well as an increasing gap over time. Conclusions: These results highlight the need for additional research on appropriate methods for modeling reading trajectories and the implications for students' response to instruction.

There are well-defined theoretical differences between the classical test theory (CTT) and item response theory (IRT) frameworks. It is understood that in the CTT framework, person and item statistics are test- and sample-dependent. This is not the perception with IRT. For this reason, the IRT framework is considered to be theoretically superior to the CTT framework for the purpose of estimating person and item parameters. In previous simulation studies, IRT models were used both as generating and as fitting models. Hence, results favoring the IRT framework could be attributed to IRT being the data-generation framework. Moreover, previous studies only considered the traditional CTT framework for the comparison, yet there is considerable literature suggesting that it may be more appropriate to use CTT statistics based on an underlying normal variable (UNV) assumption. The current study relates the class of CTT-based models with the UNV assumption to that of IRT, using confirmatory factor analysis to delineate the connections. A small Monte Carlo study was carried out to assess the comparability between the item and person statistics obtained from the frameworks of IRT and CTT with UNV assumption. Results show the frameworks of IRT and CTT with UNV assumption to be quite comparable, with neither framework showing an advantage over the other.

The latent growth curve modeling (LGM) and random effects modeling (REM) frameworks are analytically and empirically equivalent for intrinsically linear models and used interchangeably for intrinsically nonlinear models. However, while LGM provides overall model fit indices, REM does not. Overall model fit indices are useful because they evaluate how well a specified model fits data. This paper proposes to translate model fit concepts from LGM to REM to help researchers compute overall model fit indices, including the model chi-square ( χ 2 ), comparative fit index (CFI), root mean squared error of approximation (RMSEA), and standardized root mean squared residual (SRMR). Three empirical examples were used as illustrations. [ABSTRACT FROM AUTHOR]

Latent growth curve models with piecewise functions are flexible and useful analytic models for investigating individual behaviors that exhibit distinct phases of development in observed variables. As an extension of this framework, this study considers a piecewise linear-linear latent growth mixture model (LGMM) for describing segmented change of individual behavior over time where the data come from a mixture of two or more unobserved subpopulations (i.e., latent classes). Thus, the focus of this article is to illustrate the practical utility of piecewise linear-linear LGMM and then to demonstrate how this model could be fit as one of many alternatives--including the more conventional LGMMs with functions such as linear and quadratic. To carry out this study, data ("N" = 214) obtained from a procedural learning task research were used to fit the three alternative LGMMs: (a) a two-class LGMM using a linear function, (b) a two-class LGMM using a quadratic function, and (c) a two-class LGMM using a piecewise linear-linear function, where the time of transition from one phase to another (i.e., knot) is not known a priori, and thus is a parameter to be estimated.

Nonlinear mixed-effects models (NLMEMs) allow researchers to model curvilinear patterns of growth, but there is ambiguity as to what functional form the data follow. Often, researchers fit multiple nonlinear functions to data and use model selection criteria to decide which functional form fits the data "best." Frequently used model selection criteria only account for the number of parameters in a model but overlook the complexity of intrinsically nonlinear functional forms. This can lead to overfitting and hinder the generalizability and reproducibility of results. The primary goal of this study was to evaluate the performance of eight model selection criteria via a Monte Carlo simulation study and assess under what conditions these criteria are sensitive to model overfitting as it relates to functional form complexity. Results highlighted criteria with the potential to capture overfitting for intrinsically nonlinear functional forms for NLMEMs. Information criteria and the stochastic information complexity criterion recovered the true model more often than the average or conditional concordance correlation. Results also suggest that the amount of residual variance and sample size have an impact on model selection for NLMEMs. Implications for future research and recommendations for application are also provided. [ABSTRACT FROM AUTHOR]

The development and initial psychometric investigation of the Dating Attitudes Inventory (DAI) is reported. The DAI was created, to fill a gap in the literature and to measure specific masculine ideology and traditional gender attitudes that rationalize the abuse of women. Using a sample (n = 164) of male college students, a 20-item measure was developed consisting of two subscales (Rationalization of Abuse and Dominance and Control) and a total score. The 20-item DAI and other measures used for validation were completed by 216 male college students. The DAI correlated in theoretically expected ways with measures of propensity for abusiveness, relational dominance, and masculine gender role stress. A confirmatory factor analysis supported the two theorized factors of the DAI. Results of the present study offer initial support for the validity and reliability of the DAI. The authors discuss the importance of measuring masculine gender role attitudes and beliefs that support and rationalize dating violence. (Contains 4 tables.)

A conditionally linear mixed effects model is an appropriate framework for investigating nonlinear change in a continuous latent variable that is repeatedly measured over time. The efficacy of the model is that it allows parameters that enter the specified nonlinear time-response function to be stochastic, whereas those parameters that enter in a nonlinear manner are common to all subjects. In this article we describe how a variant of the Michaelis-Menten (M-M) function can be fit within this modeling framework using M"plus" 6.0. We demonstrate how observed and latent covariates can be incorporated to help explain individual differences in growth characteristics. Features of the model including an explication of key analytic decision points are illustrated using longitudinal reading data. To aid in making this class of models accessible, annotated M"plus" code is provided. (Contains 4 tables, 3 figures and 6 footnotes.)