Using SAS PROC CALIS to fit Level-1 error covariance structures of latent growth models

In the present article, we demonstrates the use of SAS PROC CALIS to fit various types of Level-1 error covariance structures of latent growth models (LGM). Advantages of the SEM approach, on which PROC CALIS is based, include the capabilities of modeling the change over time for latent constructs, measured by multiple indicators; embedding LGM into a larger latent variable model; incorporating measurement models for latent predictors; and better assessing model fit and the flexibility in specifying error covariance structures. The strength of PROC CALIS is always accompanied with technical coding work, which needs to be specifically addressed. We provide a tutorial on the SAS syntax for modeling the growth of a manifest variable and the growth of a latent construct, focusing the documentation on the specification of Level-1 error covariance structures. Illustrations are conducted with the data generated from two given latent growth models. The coding provided is helpful when the growth model has been well determined and the Level-1 error covariance structure is to be identified.     

Analysis of multivariate mixed longitudinal data: A flexible latent process approach

Multivariate ordinal and quantitative longitudinal data measuring the same latent construct are frequently collected in psychology. We propose an approach to describe change over time of the latent process underlying multiple longitudinal outcomes of different types (binary, ordinal, quantitative). By relying on random‐effect models, this approach handles individually varying and outcome‐specific measurement times. A linear mixed model describes the latent process trajectory while equations of observation combine outcome‐specific threshold models for binary or ordinal outcomes and models based on flexible parameterized non‐linear families of transformations for Gaussian and non‐Gaussian quantitative outcomes. As models assuming continuous distributions may be also used with discrete outcomes, we propose likelihood and information criteria for discrete data to compare the goodness of fit of models assuming either a continuous or a discrete distribution for discrete data. Two analyses of the repeated measures of the Mini‐Mental State Examination, a 20‐item psychometric test, illustrate the method. First, we highlight the usefulness of parameterized non‐linear transformations by comparing different flexible families of transformation for modelling the test as a sum score. Then, change over time of the latent construct underlying directly the 20 items is described using two‐parameter longitudinal item response models that are specific cases of the approach.     

Relating latent class membership to external variables: An overview

In this article we provide an overview of existing approaches for relating latent class membership to external variables of interest. We extend on the work of Nylund-Gibson et al. (Structural Equation Modeling: A Multidisciplinary Journal, 2019, 26, 967), who summarize models with distal outcomes by providing an overview of most recommended modeling options for models with covariates and larger models with multiple latent variables as well. We exemplify the modeling approaches using data from the General Social Survey for a model with a distal outcome where underlying model assumptions are violated, and a model with multiple latent variables. We discuss software availability and provide example syntax for the real data examples in Latent GOLD.     

The ABC’s of LGM: An Introductory Guide to Latent Variable Growth Curve Modeling

In recent years, we have witnessed an increase in the complexity of theoretical models that attempt to explain behavior from both contextual and developmental perspectives. This increase in the complexity of our theoretical propositions regarding behavior parallels recent methodological advances for the analysis of change. These new analysis techniques have fundamentally altered how we conceptualize and study change. Researchers have begun to identify larger frameworks to integrate our knowledge regarding the analysis of change. One such framework is latent growth modeling, perhaps the most important and influential statistical revolution to have recently occurred in the social and behavioral sciences. This study presents a basic introduction to a latent growth modeling approach for analyzing repeated measures data. Included is the specification and interpretation of the growth factors, primary extensions such as the analysis of growth in multiple populations, and structural models including both precursors of growth, and subsequent outcomes hypothesized to be influenced by the growth functions.     

Latent Growth Modeling for Logistic Response Functions

Throughout much of the social and behavioral sciences, latent growth modeling (latent curve analysis) has become an important tool for understanding individuals' longitudinal change. Although nonlinear variations of latent growth models appear in the methodological and applied literature, a notable exclusion is the treatment of growth following logistic (sigmoidal; S-shape) response functions. Such trajectories are assumed in a variety of psychological and educational settings where learning occurs over time, and yet applications using the logistic model in growth modeling methodology have been sparse. The logistic function, in particular, may not be utilized as often because software options remain limited. In this article we show how a specialized version of the logistic function can be modeled using conventional structural equation modeling software. The specialization is a reparameterization of the logistic function whose new parameters correspond to scientifically interesting characteristics of the growth process. In addition to providing an example using simulated data, we show how this nonlinear functional form can be fit using transformed subject-level data obtained through a learning task from an air traffic controller simulation experiment. LISREL syntax for the empirical example is provided.     

Growth modeling with nonignorable dropout: alternative analyses of the STAR*D antidepressant trial

This article uses a general latent variable framework to study a series of models for nonignorable missingness due to dropout. Nonignorable missing data modeling acknowledges that missingness may depend not only on covariates and observed outcomes at previous time points as with the standard missing at random assumption, but also on latent variables such as values that would have been observed (missing outcomes), developmental trends (growth factors), and qualitatively different types of development (latent trajectory classes). These alternative predictors of missing data can be explored in a general latent variable framework with the Mplus program. A flexible new model uses an extended pattern-mixture approach where missingness is a function of latent dropout classes in combination with growth mixture modeling. A new selection model not only allows an influence of the outcomes on missingness but allows this influence to vary across classes. Model selection is discussed. The missing data models are applied to longitudinal data from the Sequenced Treatment Alternatives to Relieve Depression (STAR*D) study, the largest antidepressant clinical trial in the United States to date. Despite the importance of this trial, STAR*D growth model analyses using nonignorable missing data techniques have not been explored until now. The STAR*D data are shown to feature distinct trajectory classes, including a low class corresponding to substantial improvement in depression, a minority class with a U-shaped curve corresponding to transient improvement, and a high class corresponding to no improvement. The analyses provide a new way to assess drug efficiency in the presence of dropout.     

Statistical and substantive checking in growth mixture modeling: comment on Bauer and Curran (2003)

This commentary discusses the D. J. Bauer and P. J. Curran (2003) investigation of growth mixture modeling. Single-class modeling of nonnormal outcomes is compared with modeling with multiple latent trajectory classes. New statistical tests of multiple-class models are discussed. Principles for substantive investigation of growth mixture model results are presented and illustrated by an example of high school dropout predicted by low mathematics achievement development in Grades 7-10.     

Measuring Five Dimensions of Religiosity Across Adolescence

This paper theorizes and tests a latent variable model of adolescent religiosity in which five dimensions of religiosity are interrelated: religious beliefs, religious exclusivity, external practice, private practice, and religious salience. Research often theorizes overlapping and independent influences of single items or dimensions of religiosity on outcomes such as adolescent sexual behavior, but rarely operationalizes the dimensions in a measurement model accounting for their associations with each other and across time. We use longitudinal structural equation modeling with latent variables to analyze data from two waves of the National Study of Youth and Religion. We test our hypothesized measurement model as compared to four alternate measurement models and find that our proposed model maintains superior fit. We then discuss the associations between the five dimensions of religiosity we measure and how these change over time. Our findings suggest how future research might better operationalize multiple dimensions of religiosity in studies of the influence of religion in adolescence.     

The Canberra Longitudinal Study: Design,Aims, Methodology,Outcomes and Recent Empirical Investigations

The first section of this paper describes methodology and major cognitive outcomes of the Canberra Longitudinal Study (CLS). This community study of 1045 Australians aged 70 years or over commenced in 1990. Participants were reassessed on three subsequent occasions. Its major themes were investigations of prevalence of dementia and depression, risk factors, inter-individual variability and instrument development. Over 60 papers arising from the study have been published.

The second section of this paper describes the use of a Factor of Curves (FOC) latent growth model to examine the existence of a common factor responsible for age-related deterioration in cognitive and non-cognitive processes. This analysis is a logical progression in a series of investigations using the Canberra Longitudinal Study into risk factors and correlates of cognitive change using structural equation modeling techniques. The FOC model is described and is used to explore the nature of an hypothesized common factor and to determine its relationship with age, gender, education, pre-morbid intelligence and to the ApoE genotype. Latent growth models were developed for each of reaction time, Symbol Letter Modalities Test (SLMT), Grip strength, self-reported Sensory disability and memory from three waves of data. Second-order latent level slope factors were established based on the individual factor growth curve models. Although a common factor model could be fitted to the data, there is little support that it represents a single common cause.     

Examining Spirituality Over Time: Latent Growth Curve and Individual Growth Curve Analyses

SUMMARY

Research on spirituality and religiousness has gained growing attention in recent years; however, most studies have used cross-sectional designs. As research on this topic evolves, there has been increasing recognition of the need to examine these constructs and their effects through the use of longitudinal designs. Beyond repeated-measures ANOVA and OLS regression models, what tools are available to examine these constructs over time? The purpose of this paper is to provide an overview of two cutting-edge statistical techniques that will facilitate longitudinal investigations of spirituality and religiousness: latent growth curve analysis using structural equation modeling (SEM) and individual growth curve models. The SEM growth curve approach examines change at the group level, with change over time expressed as a single latent growth factor. In contrast, individual growth curve models consider longitudinal change at the level of the person. While similar results may be obtained using either method, researchers may opt for one over the other due to the strengths and weaknesses associated with these methods. Examples of applications of both approaches to longitudinal studies of spirituality and religiousness are presented and discussed, along with design and data considerations when employing these modeling techniques.     

Structural equation models of sexual harassment: longitudinal explorations and cross-sectional generalizations

Sexual harassment and its corresponding outcomes develop and change over time, yet research on this issue has been limited primarily to cross-sectional data. In this article, longitudinal models of harassment were proposed and empirically evaluated via structural equations modeling using data from 217 women who responded to a computerized questionnaire in 1994 and again in 1996. Results indicate that sexual harassment influences both proximal and distal work-related variables (e.g., job satisfaction, work withdrawal, job withdrawal) and psychological outcomes (e.g., life satisfaction, psychological well-being, distress). In addition, a replication of the L. F. Fitzgerald, F. Drasgow, C.L. Hulin, M.J. Gelfand, and V.J. Magley (1997) model of harassment was supported. This research was an initial attempt to develop integrated models of the dynamic effects of sexual harassment over time.     

新世纪20年国内心理统计方法研究回顾

新世纪头20年, 国内心理学11本专业期刊一共发表了213篇统计方法研究论文。研究范围主要包括以下10类(按论文篇数排序)：结构方程模型、测验信度、中介效应、效应量与检验力、纵向研究、调节效应、探索性因子分析、潜在类别模型、共同方法偏差和多层线性模型。对各类做了简单的回顾与梳理。结果发现, 国内心理统计方法研究的广度和深度都不断增加, 研究热点在相互融合中共同发展; 但综述类论文比例较大, 原创性研究论文比例有待提高, 研究力量也有待加强。     

The construct of psychophysiological reactivity: Statistical and psychometric issues

The purpose of this paper is to review major statistical and psychometric issues impacting the study of psychophysiological reactivity and discuss their implications for applied developmental researchers. We first cover traditional approaches such as the observed difference score (DS) and the observed residual score (RS), including a review of classic and recent research on their reliability and validity from two related bodies of work: the measurement of change and the Law of Initial Values. Second, we review several types of latent variable modeling in this context: latent difference score (LDS) models, latent residual score (LRS) models, latent state-trait (LST) models, and latent growth curve (LGC) models. Finally, we provide broad guidelines for applied researchers broken down by key stages of a psychophysiological project: study planning, data analysis, and reporting of results. Our recommendations highlight the need for (1) increased attention to the ubiquitous nature of measurement error in observed variables and the importance of employing latent variable models when possible, and (2) increased specification of theories relating to the construct of reactivity, especially in regards to the distinction between baseline arousal and change over time in broader systems of variables.     

A joint modeling framework of responses and response times to assess learning outcomes

Abstract

A general modeling framework of response accuracy and response times is proposed to track skill acquisition and provide additional diagnostic information on the change of latent speed in a learning environment. This framework consists of two types of models: a dynamic response model that captures the response accuracy and the change of discrete latent attribute profile upon factors such as practice, intervention effects, and other latent and observable covariates, and a dynamic response time model that describes the change of the continuous response latency due to change of latent attribute profile. These two types of models are connected through a parameter, describing the change rate of the latent speed through the learning process, and a covariate defined as a function of the latent attribute profile. A Bayesian estimation procedure is developed to calibrate the model parameters and measure the latent variables. The estimation algorithm is evaluated through several simulation studies under various conditions. The proposed models are applied to a real data set collected through a spatial rotation diagnostic assessment paired with learning tools.     

Mixture Modeling Methods for the Assessment of Normal and Abnormal Personality,Part II: Longitudinal Models

Studying personality and its pathology as it changes, develops, or remains stable over time offers exciting insight into the nature of individual differences. Researchers interested in examining personal characteristics over time have a number of time-honored analytic approaches at their disposal. In recent years there have also been considerable advances in person-oriented analytic approaches, particularly longitudinal mixture models. In this methodological primer we focus on mixture modeling approaches to the study of normative and individual change in the form of growth mixture models and ipsative change in the form of latent transition analysis. We describe the conceptual underpinnings of each of these models, outline approaches for their implementation, and provide accessible examples for researchers studying personality and its assessment.     

On structural models for analyzing change

The recommendation to base the analysis of multi-wave data upon explicit models for change is advocated. Several univariate and multivariate models are described, which emerge from an interaction between the classical test theory and the structural equation modeling approach. The resulting structural models for analyzing change reflect in some of their parameters substantively interesting aspects of intra- and interindividual change in follow-up studies. The models are viewed as an alternative to an ANOVA-based analysis of longitudinal data, and are illustrated on data from a cognitive intervention study of old adults (Bakes et al , 1986). The approach presents a useful means of analyzing change over time, and is applicable for purposes of (latent) growth curve analysis when analysis of variance assumptions are violated (e.g., Schaie & Hertzog, 1982; Morrison, 1976).     

Association between Depressive Symptoms and Negative Dependent Life Events from Late Childhood to Adolescence

The association between stressful life events and depression has been consistently supported in the literature; however, studies of the developmental trajectories of these constructs and the nature of their association over time are limited. We examined trajectories of depressive symptoms and negative dependent life events and the associations between these constructs in a sample of 916 youth assessed annually from age 9 to 16, using latent growth curve modeling. Youth depressive symptoms, as rated by youth, parents, and teachers, decreased from late childhood into adolescence, whereas rates of youth-rated life events did not change significantly over time. Initial levels of depressive symptoms were positively associated with initial levels of life events. Furthermore, after controlling for the initial association between the two constructs, increases in depressive symptoms (as assessed by parents and youth) were positively associated with increases in life events over time. The study builds on prior research by focusing specifically on negative dependent life events, examining results across multiple informants, and employing latent growth curve modeling to evaluate associations between trajectories of life events and depressive symptoms in a longitudinal adolescent sample. Additional studies employing latent growth modeling to examine the changes in this association during adolescence are needed.     

Assessing psychological change in adulthood: an overview of methodological issues

This article reviews the current status of methods available for the analysis of psychological change in adulthood and aging. Enormous progress has been made in designing statistical models that can capture key aspects of intraindividual change, as reflected in techniques such as latent growth curve models and multilevel (random-effects) models. However, the rapid evolution of statistical innovations may have obscured the critical importance of addressing rival explanations for statistical outcomes, such as cohort differences or practice effects that could influence estimates of age-related change. Choice of modeling technique and implementation of a specific modeling approach should be grounded in and reflect both the theoretical nature of the developmental phenomenon and the features of the sampling design that selected persons, variables, and contexts for empirical observation.