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.     

采用词表法变式研究指向遗忘现象

在组内设计的词表法变式任务中,词表一的项目按语义或知觉特征分为遗忘项和记住项,中间指导语要求被试遗忘词表一某类项目的同时记住另一类项目,指向遗忘效应以词表一记住项与遗忘项的差异来反映。实验一中,词表一项目按语义性质分为记住项和遗忘项,结果显示:与控制组比较,标准词表法实验组词表一记忆受损显著,出现传统意义上的指向遗忘效应;变式实验组词表一记忆部分受损,与控制组差异接近.05显著水平;标准词表法实验组以及变式实验组词表二都没有表现出记忆获益;另外,变式实验组词表一记住项与遗忘项之间差异显著,反映出遗忘指导语效应。实验二发现:在变式任务中,指定被试遗忘词表一某种语义性质的项目,结果出现遗忘指导语效应;但是,在指定被试遗忘某种颜色项目时,结果没有出现遗忘指导语效应。变式任务结果比较好地支持提取抑制理论;同时也反映出,词表一记住项与遗忘项之间的区分度是影响变式情境下指向遗忘效应的重要因素。     

Implementing continuous non-normal skewed distributions in latent growth mixture modeling: An assessment of specification errors and class enumeration

Abstract

Recent advances have allowed for modeling mixture components within latent growth modeling using robust, skewed mixture distributions rather than normal distributions. This feature adds flexibility in handling non-normality in longitudinal data, through manifest or latent variables, by directly modeling skewed or heavy-tailed latent classes rather than assuming a mixture of normal distributions. The aim of this study was to assess through simulation the potential under- or over-extraction of latent classes in a growth mixture model when underlying data follow either normal, skewed-normal, or skewed-t distributions. In order to assess this, we implement skewed-t, skewed-normal, and conventional normal (i.e., not skewed) forms of the growth mixture model. The skewed-t and skewed-normal versions of this model have only recently been implemented, and relatively little is known about their performance. Model comparison, fit, and classification of correctly specified and mis-specified models were assessed through various indices. Findings suggest that the accuracy of model comparison and fit measures are dependent on the type of (mis)specification, as well as the amount of class separation between the latent classes. A secondary simulation exposed computation and accuracy difficulties under some skewed modeling contexts. Implications of findings, recommendations for applied researchers, and future directions are discussed; a motivating example is presented using education data.     

Normalized demand for drugs and other reinforcers.

The concepts of behavioral economics have proven to be useful for understanding the environmental control of overall levels of responding for a variety of commodities, including reinforcement by drug self-administration. These general concepts have implications for the assessment of abuse liability and drug abuse intervention and the formulation of public policy on drug abuse. An essential requirement is the ability to compare the demand for different drugs directly in order to assess relative abuse liability, and to compare demand for the same drug under different environmental and biological interventions to assess their ability to reduce demand. Until now, such comparisons were hampered by the confounding effect of varying drug doses and potencies that prevent quantitative comparisons of demand elasticity--sensitivity of consumption and responding to the constraint of price (effort). In this paper we describe a procedure to normalize demand-curve analysis that permits dose- and potency-independent comparisons of demand across drugs. The procedure is shown to be effective for comparing drug demand within and across the drug classes. The technique permits a quantitative ordering of demand that is consistent with the peak levels of responding maintained by the drugs. The same technique is generalized for the comparison of other types of reinforcers under different biological conditions.     

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).     

Joint consistency of nonparametric item characteristic curve and ability estimation

The simultaneous and nonparametric estimation of latent abilities and item characteristic curves is considered. The asymptotic properties of ordinal ability estimation and kernel smoothed nonparametric item characteristic curve estimation are investigated under very general assumptions on the underlying item response theory model as both the test length and the sample size increase. A large deviation probability inequality is stated for ordinal ability estimation. The mean squared error of kernel smoothed item characteristic curve estimates is studied and a strong consistency result is obtained showing that the worst case error in the item characteristic curve estimates over all items and ability levels converges to zero with probability equal to one.     

Time ordering in frontal lobe patients: a stochastic model approach

Frontal lobe patients reproduced a sequence of capital letters or abstract shapes. Immediate and delayed reproduction trials allowed the analysis of short- and long-term memory for time order by means of suitable Markov chain stochastic models. Patients were as proficient as healthy subjects on the immediate reproduction trial, thus showing spared encoding and short-term memory. They failed, instead, on the delayed trials with capital letters, but not with random shapes, suggesting that their long-term memory impairment did not depend on primary deficits for ordering, but on inability to benefit from the organisational strategies that improve the retention and retrieval in normal subjects.     

Dyadic longitudinal models: A critical review

In this review, we discuss the most commonly used models to analyze dyadic longitudinal data. We start the review with a definition of dyadic longitudinal data that allows relationship researchers to identify when these models might be appropriate. Then, we go on to describe the three major models commonly used when one has dyadic longitudinal data: the dyadic growth curve model (DGCM), the actor–partner interdependence model (APIM), and the common fate growth model (CFGM). We discuss when each model might be used and strengths and weaknesses of each model. We end with additional thoughts that focus on extensions to new methods being discussed in the literature, along with some of the challenges of collecting and analyzing dyadic longitudinal data that might be helpful for future dyadic researchers.     

Age trends in HEXACO-PI-R self-reports

We examined age differences in the six broad HEXACO personality factors and their defining facets, using self-reports from an online sample (N ≈ 100,000, ages 14–74). Honesty-Humility showed an upward trend of about one full standard deviation unit between ages 18 and 60. Age trends for Emotionality and Extraversion differed by facet, but overall were downward for Emotionality and upward for Extraversion. Agreeableness showed relatively weak age trends. Conscientiousness and Openness showed upward age trends during the teen years (extending to the mid-20s for Conscientiousness), but age trends thereafter differed considerably by facet. Results are discussed in relation to previous findings for the Big Five, to the “age-crime curve”, and to possible evolved developmental origins.