Nidhi Kohli

Modeling Growth in Latent Variables Using a Piecewise Function.

Latent growth curve models with piecewise functions for continuous repeated measures data have become increasingly popular and versatile tools for investigating individual behavior that exhibits distinct phases of development in observed variables. 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 conditions. Second, an empirical example using longitudinal reading data is fitted via maximum likelihood and results discussed. Mplus (Version 6.1) code is provided in Appendix C to aid in making this class of models accessible to practitioners.

Fitting a linear-linear piecewise growth mixture model with unknown knots: A comparison of two common approaches to inference.

A linear-linear piecewise growth mixture model (PGMM) is appropriate for analyzing segmented (disjointed) change in individual behavior over time, where the data come from a mixture of 2 or more latent classes, and the underlying growth trajectories in the different segments of the developmental process within each latent class are linear. A PGMM allows the knot (change point), the time of transition from 1 phase (segment) to another, to be estimated (when it is not known a priori) along with the other model parameters. To assist researchers in deciding which estimation method is most advantageous for analyzing this kind of mixture data, the current research compares 2 popular approaches to inference for PGMMs: maximum likelihood (ML) via an expectation-maximization (EM) algorithm, and Markov chain Monte Carlo (MCMC) for Bayesian inference. Monte Carlo simulations were carried out to investigate and compare the ability of the 2 approaches to recover the true parameters in linear-linear PGMMs with unknown knots. The results show that MCMC for Bayesian inference outperformed ML via EM in nearly every simulation scenario. Real data examples are also presented, and the corresponding computer codes for model fitting are provided in the Appendix to aid practitioners who wish to apply this class of models.

Leveraging Electronic Health Records to Develop Measurements for Processes of Care

OBJECTIVES To assess the reliability of data in electronic health records (EHRs) for measuring processes of care among primary care physicians (PCPs) and examine the relationship between these measures and clinical outcomes. DATA SOURCES/STUDY SETTING EHR data from 15,370 patients with diabetes, 49,561 with hypertension, in a group practice serving four Northern California counties. STUDY DESIGN/METHODS Exploratory factor analysis (EFA) and multilevel analyses of the relationships between processes of care variables and factor scales with control of hemoglobin A1c, blood pressure (BP), and low density lipoprotein (LDL) among patients with diabetes and BP among patients with hypertension. PRINCIPAL FINDINGS Volume of e-messages, number of days to the third-next-available appointment, and team communication emerged as reliable factors of PCP processes of care in EFA (Cronbachs alpha=0.73, 0.62, and 0.91). Volume of e-messages was associated with higher odds of LDL control (≤100) (OR=1.13, p<.05) among patients with diabetes. Frequent in-person visits were associated with better BP (OR=1.02, p<.01) and LDL control (OR=1.01, p<.01) among patients with diabetes, and better BP control (OR=1.04, p<.01) among patients with hypertension. CONCLUSIONS The EHR offers process of care measures which can augment patient-reported measures of patient-centeredness. Two of them are significantly associated with clinical outcomes. Future research should examine their association with additional outcomes.

Relationships among Classical Test Theory and Item Response Theory Frameworks via Factor Analytic Models.

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 Development and Initial Validation of the Dating Attitudes Inventory: A Measure of the Gender Context of Dating Violence in Men

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.

Piecewise Linear–Linear Latent Growth Mixture Models With Unknown Knots

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.

A Second-Order Conditionally Linear Mixed Effects Model With Observed and Latent Variable Covariates.

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 Mplus 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 Mplus code is provided.

A Finite Mixture of Nonlinear Random Coefficient Models for Continuous Repeated Measures Data

Nonlinear random coefficient models (NRCMs) for continuous longitudinal data are often used for examining individual behaviors that display nonlinear patterns of development (or growth) over time in measured variables. As an extension of this model, this study considers the finite mixture of NRCMs that combine features of NRCMs with the idea of finite mixture (or latent class) models. The efficacy of this model is that it allows the integration of intrinsically nonlinear functions where the data come from a mixture of two or more unobserved subpopulations, thus allowing the simultaneous investigation of intra-individual (within-person) variability, inter-individual (between-person) variability, and subpopulation heterogeneity. Effectiveness of this model to work under real data analytic conditions was examined by executing a Monte Carlo simulation study. The simulation study was carried out using an R routine specifically developed for the purpose of this study. The R routine used maximum likelihood with the expectation–maximization algorithm. The design of the study mimicked the output obtained from running a two-class mixture model on task completion data.

A Second-Order Longitudinal Model for Binary Outcomes: Item Response Theory Versus Structural Equation Modeling

Measuring academic growth, or change in aptitude, relies on longitudinal data collected across multiple measurements. The National Educational Longitudinal Study (NELS:88) is among the earliest, large-scale, educational surveys tracking students’ performance on cognitive batteries over 3 years. Notable features of the NELS:88 data set, and of almost all repeated measures educational assessments, are (a) the outcome variables are binary or at least categorical in nature; and (b) a set of different items is given at each measurement occasion with a few anchor items to fix the measurement scale. This study focuses on the challenges related to specifying and fitting a second-order longitudinal model for binary outcomes, within both the item response theory and structural equation modeling frameworks. The distinctions between and commonalities shared between these two frameworks are discussed. A real data analysis using the NELS:88 data set is presented for illustration purposes.

FitPMM: An R Routine to Fit Finite Mixture of Piecewise Mixed-Effect Models With Unknown Random Knots

Piecewise mixed-effect models are frequently used in education and psychology to model segmented growth over time. For data that exhibit distinct phases of growth, piecewise models are attractive alternatives to familiar quadratic and higher order polynomial models because the parameters in piecewise models provide more relevant information about the mechanism underlying the change process (Fitzmaurice, Laird, & Ware, 2011). Different types of trajectories can be specified in the different phases of a piecewise model; however, a linear–linear piecewise model seems to dominate practical applications. An interesting feature of a linear–linear piecewise model is the knot, the change point on the time axis where two linear splines join (Cudeck & Harring, 2010). In many applications, practitioners locate the knot in piecewise models a priori based on the subject-matter knowledge, and the knot is assumed to be known in subsequent statistical analyses. Moreover, the knot is commonly treated as a fixed parameter, indicating that each individual’s change point is assumed to be the same. An appealing alternative model for practical applications would allow the knot in the piecewise model to be an estimable subject-specific parameter. This model is a type of nonlinear random coefficient model like that described in Cudeck and Klebe (2002) and du Toit and Cudeck (2009). A mixture component can be added to the model to relax the assumption of a single population and to allow latent subpopulations (Everitt & Hand, 1981; Harring, 2012; Kohli, Harring, & Zopluoglu, under review; Titterington, Smith, & Makov, 1985). Fitting finite mixture of nonlinear random coefficient models can be quite challenging. However, du Toit and Cudeck provided a simplified estimation scheme for models with a combination of linear and nonlinear coefficients, and finite mixture of these models can be fitted following the extension provided by Harring (2012). An R routine, fitPMM.R, was designed to fit the finite mixture of piecewise mixed-effect models with unknown random knot parameters using the estimation