This study proposed a three-stage measurement model utilizing the Latent Growth Curve Modeling and Latent Class Growth Analysis. The measurement model was illustrated using repeated data collected through a four-week prospective study tracking the subjective well-being of volunteer college students (n=154). Firstly, several unconditional growth…

Nonlinear mixed-effects models are models in which one or more coefficients of the growth model enter in a nonlinear manner, such as appearing in the exponent of the growth function. In their applications, the within-individual residuals are often assumed to be independent with constant variance across time, an assumption that implies that the…

Several statistical models have been developed in educational measurement to determine and track the performance of students in longitudinal studies. An example of a model designed for such purpose is the latent transition analysis (LTA) model. The LTA model (Graham, Collins, Wugalter, Chung, & Hansen 1991) is a type of autoregressive model…

This study investigated the extent to which class-specific parameter estimates are biased by the within-class normality assumption in nonnormal growth mixture modeling (GMM). Monte Carlo simulations for nonnormal GMM were conducted to analyze and compare two strategies for obtaining unbiased parameter estimates: relaxing the within-class normality…

Latent curve models have become a popular approach to the analysis of longitudinal data. At the individual level, the model expresses an individual's response as a linear combination of what are called "basis functions" that are common to all members of a population and weights that may vary among individuals. This article uses…

Analysts of discrete data often face the challenge of managing the tendency of inflation on certain values. When treated improperly, such phenomenon may lead to biased estimates and incorrect inferences. This study extends the existing literature on single-value inflated models and develops a general framework to handle variables with more than…

Due to the complexity of latent transition analysis (LTA) model structure and qualitative decision making in LTA, power analysis has less been reported and studied. Baldwin (2015) and Gudicha, et al., (2016) recently reported results about power analysis in LTA, which included useful information. On the other hand, both studies are limited in the…

In this digital ITEMS module, Dr. Jeffrey Harring and Ms. Tessa Johnson introduce the linear mixed effects (LME) model as a flexible general framework for simultaneously modeling continuous repeated measures data with a scientifically defensible function that adequately summarizes both individual change as well as the average response. The module…

Piecewise GMM with unknown turning points is a new procedure to investigate heterogeneous subpopulations' growth trajectories consisting of distinct developmental phases. Unlike the conventional PGMM, which relies on theory or experiment design to specify turning points a priori, the new procedure allows for an optimal location of turning points…

Single subject (SS) designs are popular in educational and psychological research. There exist several statistical techniques designed to analyze such data and to address the question of whether an intervention has the desired impact. Recently, researchers have suggested that generalized additive models (GAMs) might be useful for modeling…

Higher education in America is characterized by widespread access to college but low rates of completion, especially among undergraduates at less selective institutions. We analyze longitudinal transcript data to examine processes leading to graduation, using Hidden Markov modeling. We identify several latent states that are associated with…

The recent change in the general social survey (GSS) to a rotating panel design is a landmark development for social scientists. Sociological methodologists have argued that fixed-effects (FE) models are generally the best starting point for analyzing panel data because they allow analysts to control for unobserved time-constant heterogeneity. We…

Cognitive diagnosis models are diagnostic models used to classify respondents into homogenous groups based on multiple categorical latent variables representing the measured cognitive attributes. This study aims to present longitudinal models for cognitive diagnosis modeling, which can be applied to repeated measurements in order to monitor…

A first-order latent growth model assesses change in an unobserved construct from a single score and is commonly used across different domains of educational research. However, examining change using a set of multiple response scores (e.g., scale items) affords researchers several methodological benefits not possible when using a single score. A…

Collection and analysis of longitudinal data is an important tool in understanding growth and development over time in a whole range of human endeavors. Ideally, researchers working in the longitudinal framework are able to collect data at more than two points in time, as this will provide them with the potential for a deeper understanding of the…