(Re)evaluating the Implications of the Autoregressive Latent Trajectory Model Through Likelihood Ratio Tests of Its Initial Conditions

The autoregressive latent trajectory (ALT) model synthesizes the autoregressive model and the latent growth curve model. The ALT model is flexible enough to produce a variety of discrepant model-implied change trajectories. While some researchers consider this a virtue, others have cautioned that this may confound interpretations of the model's parameters. In this article, we show that some—but not all—of these interpretational difficulties may be clarified mathematically and tested explicitly via likelihood ratio tests (LRTs) imposed on the initial conditions of the model. We show analytically the nested relations among three variants of the ALT model and the constraints needed to establish equivalences. A Monte Carlo simulation study indicated that LRTs, particularly when used in combination with information criterion measures, can allow researchers to test targeted hypotheses about the functional forms of the change process under study. We further demonstrate when and how such tests may justifiably be used to facilitate our understanding of the underlying process of change using a subsample (N = 3,995) of longitudinal family income data from the National Longitudinal Survey of Youth.     

Are economic conditions related to nonnormative life satisfaction development? Evaluating the relative impact of economic conditions,personality, and subjective health

This study examined the relative contribution of psychological and socioeconomic resources to explaining qualitative individual differences in life satisfaction development. We used growth mixture modeling and a cohort‐sequential design to investigate life satisfaction development from ages 25 to 65, in a nationally representative panel (the Socioeconomic Panel). Eighty‐three percent of the participants experienced stability in life satisfaction. In a subgroup of individuals (10%), life satisfaction declined. This subgroup lived under less favorable economic conditions and reported downward moves on an index of socioeconomic status. In another subgroup (7%), life satisfaction was low at age 25 and increased up to age 65. This group was also socioeconomically disadvantaged but scored higher on adaptive personality traits and experienced upward social mobility. Generally, personality traits explained level differences in life satisfaction better than economic conditions. However, economic conditions explained nonnormative life satisfaction development better than generalized control beliefs and the Big Five traits.     

LGM模型中缺失数据处理方法的比较:ML方法与Diggle-Kenward选择模型

追踪研究中缺失数据十分常见。本文通过Monte Carlo模拟研究,考察基于不同前提假设的Diggle-Kenward选择模型和ML方法对增长参数估计精度的差异,并考虑样本量、缺失比例、目标变量分布形态以及不同缺失机制的影响。结果表明:(1)缺失机制对基于MAR的ML方法有较大的影响,在MNAR缺失机制下,基于MAR的ML方法对LGM模型中截距均值和斜率均值的估计不具有稳健性。(2)DiggleKenward选择模型更容易受到目标变量分布偏态程度的影响,样本量与偏态程度存在交互作用,样本量较大时,偏态程度的影响会减弱。而ML方法仅在MNAR机制下轻微受到偏态程度的影响。     

Identifying “types” of ideologies and intergroup biases: Advancing a person-centred approach to social psychology

Whether it be those who are “high” on right-wing authoritarianism (RWA) and social dominance orientation (SDO), or a mixture of “low” on explicit, but “high” on implicit, bias, many social psychological theories predict the existence of distinct “types” of people. These assumptions are, however, untestable using variable-centred analyses. Accordingly, we argue that the time has come to utilise person-centred analyses that enable us to test these key assumptions. We open by demonstrating how to implement – and interpret – latent profile analysis (a type of person-centred analysis), using RWA and SDO as an example. We then discuss the debate over the dimensionality of political ideology to highlight the need for person-centred analyses. Next, we review person-centred approaches to political ideology and highlight recent work using person-centred analyses to assess key assumptions of ambivalent sexism and relative deprivation. We conclude by discussing limitations to person-centred approaches and by providing suggestions for future research.     

Set points of positivity ratio for different levels of well‐being: A latent profile analysis

Previous studies have explored the set points of the positivity ratio by grouping according to predetermined cut‐off scores, resulting in inconsistent criteria and unstable results. This study intends to further explore the set points of the positivity ratio using latent profile analysis. Two samples of 716 college students and 381 adults in China completed the Questionnaire for Eudaimonic Well‐Being, the Personal Growth Subscale from Ryff's Psychological Well‐being Scale, the Need Satisfaction Questionnaire, and the Emotional Experience of Well‐Being Questionnaire. College students were classified into four classes (2.0, 2.8, 3.7 and 5.0) with the set points of the positivity ratio, whereas adults were classified into three classes (1.9, 2.9 and 4.2) with the set points of the positivity ratio. The difference of the set points between college students and adults was nonsignificant for medium and high well‐being classes, and significant with a small effect size for the higher well‐being class. Future research should examine more diverse samples and combine the real experience method to further explore the set points of the positivity ratio.     

类别变量的中介效应分析

在心理学和其他社科研究领域,研究者能熟练地进行连续变量的中介效应分析,但面对自变量、中介变量或(和)因变量为类别变量的中介效应分析,研究者往往束手无策。在阐述类别自变量中介分析方法的基础上,我们建议使用整体和相对中介相结合的类别自变量中介分析方法,并给出了分析流程。以二分因变量为例,讨论了中介变量或(和)因变量为类别变量的中介分析方法的发展过程(即尺度统一的过程),建议通过检验Za×Zb的显著性来判断中介效应的显著性。用二个实际例子演示如何进行类别变量的中介效应分析。最后展望了类别变量的中介效应分析研究的拓展方向。     

Model Evaluation and Multiple Strategies in Cognitive Diagnosis: An Analysis of Fraction Subtraction Data

This paper studies three models for cognitive diagnosis, each illustrated with an application to fraction subtraction data. The objective of each of these models is to classify examinees according to their mastery of skills assumed to be required for fraction subtraction. We consider the DINA model, the NIDA model, and a new model that extends the DINA model to allow for multiple strategies of problem solving. For each of these models the joint distribution of the indicators of skill mastery is modeled using a single continuous higher-order latent trait, to explain the dependence in the mastery of distinct skills. This approach stems from viewing the skills as the specific states of knowledge required for exam performance, and viewing these skills as arising from a broadly defined latent trait resembling the θ of item response models. We discuss several techniques for comparing models and assessing goodness of fit. We then implement these methods using the fraction subtraction data with the aim of selecting the best of the three models for this application. We employ Markov chain Monte Carlo algorithms to fit the models, and we present simulation results to examine the performance of these algorithms. The work reported here was performed under the auspices of the External Diagnostic Research Team funded by Educational Testing Service. Views expressed in this paper does not necessarily represent the views of Educational Testing Service.     

A Note on “Constant Latent Odds-Ratios Models and the Mantel–Haenszel Null Hypothesis” Hessen, 2005

In a recent paper, Hessen (Psychometrika 70(3):497–516, 2005) introduces the class of constant latent odds-ratios models as an extension of the Rasch model for which the sum score is still the sufficient statistic for ability. In this paper the relation between both the general and the general parametric constant latent odds-ratios model and the Rasch model is considered.     

Latent Class Models for Diary Method Data: Parameter Estimation by Local Computations

The increasing use of diary methods calls for the development of appropriate statistical methods. For the resulting panel data, latent Markov models can be used to model both individual differences and temporal dynamics. The computational burden associated with these models can be overcome by exploiting the conditional independence relations implied by the model. This is done by associating a probabilistic model with a directed acyclic graph, and applying transformations to the graph. The structure of the transformed graph provides a factorization of the joint probability function of the manifest and latent variables, which is the basis of a modified and more efficient E-step of the EM algorithm. The usefulness of the approach is illustrated by estimating a latent Markov model involving a large number of measurement occasions and, subsequently, a hierarchical extension of the latent Markov model that allows for transitions at different levels. Furthermore, logistic regression techniques are used to incorporate restrictions on the conditional probabilities and to account for the effect of covariates. Throughout, models are illustrated with an experience sampling methodology study on the course of emotions among anorectic patients. Frank Rijmen was partly supported by the Fund for Scientific Research Flanders (FWO).