On the power of multivariate latent growth curve models to detect correlated change

We evaluated the statistical power of single-indicator latent growth curve models (LGCMs) to detect correlated change between two variables (covariance of slopes) as a function of sample size, number of longitudinal measurement occasions, and reliability (measurement error variance). Power approximations following the method of Satorra and Saris (1985) were used to evaluate the power to detect slope covariances. Even with large samples (N = 500) and several longitudinal occasions (4 or 5), statistical power to detect covariance of slopes was moderate to low unless growth curve reliability at study onset was above .90. Studies using LGCMs may fail to detect slope correlations because of low power rather than a lack of relationship of change between variables. The present findings allow researchers to make more informed design decisions when planning a longitudinal study and aid in interpreting LGCM results regarding correlated interindividual differences in rates of development.     

Bayesian power equivalence in latent growth curve models

Longitudinal studies are the gold standard for research on time-dependent phenomena in the social sciences. However, they often entail high costs due to multiple measurement occasions and a long overall study duration. It is therefore useful to optimize these design factors while maintaining a high informativeness of the design. Von Oertzen and Brandmaier (2013,Psychology and Aging, 28, 414) applied power equivalence to show that Latent Growth Curve Models (LGCMs) with different design factors can have the same power for likelihood-ratio tests on the latent structure. In this paper, we show that the notion of power equivalence can be extended to Bayesian hypothesis tests of the latent structure constants. Specifically, we show that the results of a Bayes factor design analysis (BFDA; Schönbrodt & Wagenmakers (2018,Psychonomic Bulletin and Review, 25, 128) of two power equivalent LGCMs are equivalent. This will be useful for researchers who aim to plan for compelling evidence instead of frequentist power and provides a contribution towards more efficient procedures for BFDA.     

Latent Growth Curve and Repeated Measures ANOVA Contrasts: What the Models are Telling You

The relationship between the latent growth curve and repeated measures ANOVA models is often misunderstood. Although a number of investigators have looked into the similarities and differences among these models, a cursory reading of the literature can give the impression that they are very different models. Here we show that each model represents a set of contrasts on the occasion means. We demonstrate that the fixed effects parameters of the estimated basis vector latent growth curve model are merely a transformation of the repeated measures ANOVA fixed effects parameters. We further show that differences in fit in models that estimate the same means structure can be due to the different error covariance structures implied by the model. We show these relationships both algebraically and through using data from a simulation.     

Latent Growth Models with Floors,Ceilings, and Random Knots

In longitudinal/developmental studies, individual growth trajectories are sometimes bounded by a floor at the beginning of the observation period and/or a ceiling toward the end of the observation period (or vice versa), resulting in inherently nonlinear growth patterns. If the trajectories between the floor and ceiling are approximately linear, such longitudinal growth patterns can be described with a linear piecewise (spline) model in which segments join at knots. In these scenarios, it may be of specific interest for researchers to examine the timing when transition occurs, and in some occasions also to examine the levels of the floors and/or ceilings if they are not known and fixed. In the current study, we propose a reparameterized piecewise latent growth curve model so that a direct estimation of the random knots (and, if needed, a direct estimation of random floors and ceilings) is possible. We derive the model reparameterization using a 4-step structured latent curve modeling approach. We provide two illustrative examples to demonstrate how the proposed reparameterized models can be fitted to longitudinal growth data using the popular SEM software Mplus and we supply the full coding for applied researchers’ reference.     

Change in cognitive functioning associated with apoE genotype in a community sample of older adults

The influence of a genetic risk factor, apolipoprotein E (apoE) epsilon4 variant, was assessed in older adults aged 70 to 94 on 3 occasions over 7 years. The results of latent growth curve analyses are reported for individuals genotyped for apoE at the 2nd measurement occasion (n = 601) and for a subsample of individuals without probable or definite dementia during the 1st or 2nd occasion (n = 434). ApoE-epsilon4 status was a significant predictor of level and change in memory performance and change in speed performance in the full sample, and of initial level and change in memory performance in the nondemented subsample. These results support previous findings that apoE-epsilon4 is associated with accelerated memory deterioration in individuals without clinical dementia.     

Do you feel better or worse? The validity of perceived deviations of mood states from mood traits

The advantages of assessing self‐perceived deviations of mood states from mood traits in cross‐sectional as well as longitudinal studies are discussed in detail. The validity of self‐perceived mood deviations is analysed in a longitudinal study with three occasions of measurement and 176 participants. In order to assess self‐perceived mood deviations, participants rated the deviation of their momentary mood from how they felt in general with respect to 32 mood adjectives belonging to three mood scales (pleasant–unpleasant, calm–restless, awake–sleepy). Furthermore, mood states, mood traits, and other personality variables (hedonic level, neuroticism, extraversion, openness, agreeableness, conscientiousness) are assessed by self‐report. Using models of latent state–trait theory, it is shown that the self‐perceived mood deviation scales are reliable (reliabilities between 0.73 and 0.95) and sensitive to occasion‐specific fluctuations (occasion specificities between 0.38 and 0.72). The self‐perceived deviation scales show high correlations with latent occasion‐specific deviation variables defined on the basis of repeatedly measured mood states (high convergent validity). In contrast to self‐reported mood states, however, self‐perceived mood deviations show much smaller and in most cases non‐significant correlations with personality variables (high discriminant validity). Furthermore, it is shown that self‐perceived mood deviations can be used to suppress stable situation‐specific variance in mood traits defined as aggregated states. Therefore, it can be demonstrated that including self‐perceived mood deviations in analyses on mood–personality associations enhances the association coefficients considerably. Finally, the implications of the results for the individual assessment of mood deviations, as well as for studies on affect and personality, are discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

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.     

复杂目标实现过程中进展感知与努力的因果关系：基于潜在差分模型的分析

长期、多任务复杂目标实现过程中,个体如何依据过往进展来调节未来努力付诸程度,一直是工业与组织心理学中有争议的话题之一。本研究以创业活动作为研究背景,以PESD数据库中215名创业者为研究对象,构建潜在差分模型对连续5年的创业进展感知与创业努力的客观数据进行分析。结果显示,进展感知和努力间呈现互动式因果关系：前一期努力程度能够预测下一期进展感知的增加,但前一期进展感知却使得下一期努力程度减弱。     

Chinese college students' general and relationship‐specific representations of adult attachment: Variable‐centred and person‐centred analysis

Formerly, researchers often treated adult attachment as a trait‐like construct with consistency across relationship contexts. However, recent studies have shown that people possess multiple relationship‐specific attachment representations, and inter‐correlations among them are only in a small‐to‐medium range. The aim of this study is to test whether these variable‐centred results could be replicated in China and further supplement them with a person‐centred analysis focusing on identifying prototypical patterns of multiple working models across relationships. We administrated measurements of general and four relationship‐specific (mother/father/best friend/romantic partner) working models and indicators of psychological adjustment upon 302 Chinese college students. Results from variable‐centred analysis demonstrated the cross‐relationship variability in working models. Furthermore, global indicators of psychological adjustment were better predicted by general models, while relationship‐specific indicators were better predicted by corresponding relationship‐specific models. These results largely replicate previous Western studies, supporting the existence of multiple attachment representations in China. In person‐centred analysis, a latent profile analysis identified four typical classes of working model profiles: all‐average, all‐secure, romantic‐insecure and peer‐secure. These classes differed not only in the cross‐relationship variability of their working models, but also in their levels of psychological adjustment. These interesting patterns may have theoretical implications and are worthy of further examination.     

The Consequences of Ignoring Variability in Measurement Occasions Within Data Collection Waves in Latent Growth Models

In longitudinal data collection, it is common that each wave of collection spans several months. However, researchers using latent growth models commonly ignore variability in data collection occasions within a wave. In this study, we investigated the consequences of ignoring within-wave variability in measurement occasions using a Monte Carlo simulation and an empirical study. The results of the simulation study showed that ignoring heterogeneity resulted in biased estimates for some parameters, especially when heterogeneity was large and assessment dates had a skewed distribution. Models constructed on person-specific time points yielded precise estimates and more adequate model fit. In the empirical study, we demonstrated different time coding strategies with a subsample taken from Early Childhood Longitudinal Study Kindergarten Cohort.     

The bidirectional relation between positive mental health and psychopathology in a longitudinal representative panel study

Background: There is accumulating evidence that positive mental health and psychopathology should be seen as separate indicators of mental health. This study contributes to this evidence by investigating the bidirectional relation between positive mental health and psychopathological symptoms over time. Methods: Positive mental health (MHC-SF) and psychopathological symptoms (BSI) were longitudinally measured in a representative adult sample (N?=?1932) on four measurement occasions in nine months. A cross-lagged panel design was applied and evaluated with a latent growth model combined with an item response theory measurement model. Results: Psychopathological symptoms were longitudinally related to positive mental health and vice versa, controlling for initial levels. The changes over time were even more important than the absolute levels of psychopathological symptoms and positive mental health, respectively. Conclusions: The results underline the need for a comprehensive perspective on mental health, incorporating both the treatment of symptoms and the enhancement of well-being.     

The Other Side of Method Bias: The Perils of Distinct Source Research Designs

Common source bias has been the focus of much attention. To minimize the problem, researchers have sometimes been advised to take measurements of predictors from one observer and measurements of outcomes from another observer or to use separate occasions of measurement. We propose that these efforts to eliminate biases due to common source variance create serious problems. To demonstrate the problems of using what we term the “distinct sources” measurement design, we provide an integrative review of the literature regarding both contamination and deficiency of measures. Building on this theme, the article uses simulated data to demonstrate how using data from distinct observers or occasions of measurement can distort estimates of predictor importance at least as much as common source variance. Alternative multisource designs are advocated and examined for tractability by simulating various numbers of observations and sources in the research design.     

Investigating Ceiling Effects in Longitudinal Data Analysis

Score limitation at the top of a scale is commonly termed “ceiling effect.” Ceiling effects can lead to serious artifactual parameter estimates in most data analysis. This study examines the consequences of ceiling effects in longitudinal data analysis and investigates several methods of dealing with ceiling effects through Monte Carlo simulations and empirical data analyses. Data were simulated based on a latent growth curve model with T = 5 occasions. The proportion of the ceiling data [10%–40%] was manipulated by using different thresholds, and estimated parameters were examined for R = 500 replications. The results showed that ceiling effects led to incorrect model selection and biased parameter estimation (shape of the curve and magnitude of the changes) when regular growth curve models were applied. The Tobit growth curve model, instead, performed very well in dealing with ceiling effects in longitudinal data analysis. The Tobit growth curve model was then applied in an empirical cognitive aging study and the results were discussed.     

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。     

Multilevel Factor Analysis: Reporting Guidelines and a Review of Reporting Practices

We provide reporting guidelines for multilevel factor analysis (MFA) and use these guidelines to systematically review 72 MFA applications in journals across a range of disciplines (e.g., education, health/nursing, management, and psychology) published between 1994 and 2014. Results are organized in terms of the (a) characteristics of the MFA application (e.g., construct measured), (b) purpose (e.g., measurement validation), (c) data source (e.g., number of cases at Level 1 and Level 2), (d) statistical approach (e.g., maximum likelihood), and (e) results reported (e.g., intraclass correlations for indicators and latent variables, standardized factor loadings, fit indices). Results from this review have implications for applied researchers interested in expanding their approaches to psychometric analyses and construct validation within a multilevel framework and for methodologists using Monte Carlo methods to explore technical and methodological issues grounded in realistic research design conditions.     

A Latent Variable Framework for Power Estimation Within Intervention Contexts

This paper presents a latent growth SEM approach for the estimation of treatment effects, and power to detect such effects, within a true experimental design setting in which subjects are randomly assigned to treatment and control conditions. Power estimation is a critical component of intervention experiment design and the testing of their results. Although researchers have become increasingly sophisticated in applying tests for statistical significance in intervention contexts, few are aware of the power of these tests. The issues raised in this paper are not new; however, reminding researchers to consider these points is important. Exactly how the researcher handles these issues will depend on the questions asked and the resources available, as well as other considerations. Discussion underscores the relationship between the reliability of a study's measures and concomitant increases in power obtained within the SEM framework.     

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.     

计划缺失设计——通过有意缺失让研究更高效

缺失值是社会科学研究中非常普遍的现象。全息极大似然估计和多重插补是目前处理缺失值最有效的方法。计划缺失设计利用特殊的实验设计有意产生缺失值, 再用现代的缺失值处理方法来完成统计分析, 获得无偏的统计结果。计划缺失设计可用于横断面调查减少(或增加)问卷长度和纵向调查减少测量次数, 也可用于提高测量有效性。常用的计划缺失设计有三式设计和两种方法测量。     

Statistical power analysis for growth curve models using SAS

Power analysis is critical in research designs. This study discusses a simulation-based approach utilizing the likelihood ratio test to estimate the power of growth curve analysis. The power estimation is implemented through a set of SAS macros. The application of the SAS macros is demonstrated through several examples, including missing data and nonlinear growth trajectory situations. The results of the examples indicate that the power of growth curve analysis increases with the increase of sample sizes, effect sizes, and numbers of measurement occasions. In addition, missing data can reduce power. The SAS macros can be modified to accommodate more complex power analysis for both linear and nonlinear growth curve models.