Assessing Measurement Invariance of the Children's Depression Inventory in Chinese and Italian Primary School Student Samples

This study tested the measurement invariance of Children's Depression Inventory (CDI) and compared its factorial variance/covariance and latent means among Chinese and Italian children. Multigroup confirmatory factor analysis of the original five factors identified by Kovacs revealed that full measurement invariance did not hold. Further analysis showed that 4 of 21 factor loadings, 14 of 26 intercepts, and 12 of 26 item errors were noninvariant. Factor variance and covariance invariant tests revealed significant differences between Chinese and Italian samples. The latent factor mean comparison suggested no significant difference across the two groups. Nevertheless, the finding of partial metric and scalar invariance suggested that observed mean differences on the CDI items cannot be fully explained by the mean differences in the latent factor. These results suggest that researchers and practitioners exercise caution when gauging the size of the true national population differences in depressive symptoms among Italian and Chinese children when assessed via CDI. In addition to providing needed evidence on the use of the CDI in Italian and Chinese children specifically, the methods used in this research can serve more generally as an example for other cross-cultural assessment research to test structural equivalence and measurement invariance of scales and to determine why it is important to do so.     

Exploring social and personal relationships: The issue of measurement invariance of non‐independent observations

In social psychology, some research questions address a comparison of individuals belonging to different social or relational contexts. As measurement invariance literature has indicated, before comparing two or more groups (gender, cultures, and relationship types), the question of whether a measurement of the construct used for the comparison is invariant must be verified. Measurement invariance helps to assure the validity of the measurement and the construct equivalence across groups. However, when non‐independent data are used for comparison (the same individual provides data for his or her different relationship types), the standard multigroup analyses for testing measurement invariance are not accurate. The current study presents a modified correlated uniqueness model that may be applied in these specific cases. As an example, we analyzed the invariance of the Intimate Disclosure scale and the Conflict scale in mother–child, father–child, and romantic relationships of young adults. Results indicate a partial invariance: only configural invariance, factor loading invariance, and factor covariance invariance were found. The consequences for validity of the measurement are then discussed. Copyright © 2014 John Wiley & Sons, Ltd.     

A checklist for testing measurement invariance

The analysis of measurement invariance of latent constructs is important in research across groups, or across time. By establishing whether factor loadings, intercepts and residual variances are equivalent in a factor model that measures a latent concept, we can assure that comparisons that are made on the latent variable are valid across groups or time. Establishing measurement invariance involves running a set of increasingly constrained structural equation models, and testing whether differences between these models are significant. This paper provides a step-by-step guide to analysing measurement invariance.     

Factorial invariance and latent mean differences of scores on trait emotional intelligence across gender and age

Little is known about the factorial invariance and latent mean difference across sex and age in trait emotional intelligence (EI). The purpose of this study was to examine whether the measurement structure underlying trait EI is equivalent across sex and age groups. The sample consisted of 2919 teenagers, youths and adults. In order to investigate the above hypothesis the measurement and structural equivalence as well as the equality of latent means of scores across sex and age were tested. The multi-group confirmatory factor analysis results revealed that configural, metric, scalar and structural invariance exist across sex and age samples. Findings regarding the latent mean differences across sex and age groups are discussed with reference to recent and past findings.     

Group Differences in Regression Intercepts: Implications for Factorial Invariance

Studies of differential prediction typically examine group differences in linear regression slopes or intercepts for predicting criterion scores from one or more test scores. When there are no group differences in slopes, what are the implications of differences in regression intercepts for the measurement equivalence of the tests or criterion across groups? Measurement equivalence is here defined as factorial invariance under a single-factor model for the tests and criterion. Two theorems are given that describe conditions under which intercept differences can exist under factorial invariance. In such cases, intercept differences do not result from measurement bias in either the tests or criterion. The conditions of the theorems are testable using multiple-group confirmatory factor analysis. These test procedures are illustrated in real data. The implications of the theorems and the test procedures for studies of differential prediction are discussed.     

Age-related invariance of abilities measured with the Wechsler Adult Intelligence Scale--III

Examination of measurement invariance tests the assumption that the model underlying a set of test scores is directly comparable across groups. The observation of measurement invariance provides fundamental evidence for the inference that scores on a test afford equivalent measurement of the same psychological traits among diverse groups. Groups may be derived from different psychosocial backgrounds or different clinical presentations. In the Wechsler Adult Intelligence Scale-III (WAIS-III)/Wechsler Memory Scale-III (WMS-III) Technical Manual (Psychological Corporation, 2002), there appears to be a breakdown in factor structure among the standardization cases in older adults. In this study, the authors evaluated the invariance of the measurement model of the WAIS-III across 5 age bands. All components of the measurement model were examined. Overall, the evidence pointed to invariance across age of a modified 4-factor model that included cross-loadings for the Similarities and Arithmetic subtests. These results support the utility of the WAIS-III as a measure of stable intelligence traits across a wide age range.     

Factor structure, measurement invariance and structural invariance of the MSCEIT V2.0

This study explored factor structure and measurement and structural invariance of the MSCEIT V2.0 across two age groups: 258 young (18-31 years) and 262 older adults (32-79 years). Results supported a three-factor solution reflecting the Experiential Emotional Intelligence area, and Understanding Emotions and Managing Emotions branches. There was evidence of measurement invariance of factor structure and factor loadings, and partial support for invariance of the intercepts. Comparisons of latent factor means suggested that older adults have significantly higher mean scores on two of the three factors: Understanding and Managing Emotions. Implications of the invariance tests and latent means analyses are discussed.     

Factorial structure and age-related psychometrics of the MIDUS personality adjective items across the life span

The present study addresses issues of measurement invariance and comparability of factor parameters of Big Five personality adjective items across age. Data from the Midlife in the United States (MIDUS) survey were used to investigate age-related developmental psychometrics of the MIDUS personality adjective items in 2 large cross-sectional samples (exploratory sample: N = 862; analysis sample: N = 3,000). After having established and replicated a comprehensive 5-factor structure of the measure, increasing levels of measurement invariance were tested across 10 age groups. Results indicate that the measure demonstrates strict measurement invariance in terms of number of factors and factor loadings. Also, we found that factor variances and covariances were equal across age groups. By contrast, a number of age-related factor mean differences emerged. The practical implications of these results are discussed, and future research is suggested.     

Measurement invariance of WISC-IV across normative and clinical samples

Measurement invariance of the WISC-IV second-order factorial structure between normative and clinical samples was investigated using WISC-IV core subtests and a total of 1100 children aged 6-16. Multi-group higher order analysis of mean and covariance structure (MG-MACS) models were used to analyze these data. Results supported measurement invariance. Only Coding and Comprehension subtest intercepts varied slightly between groups. The hypothesized WISC-IV factor model described the data well. Factor patterns, first- and second-order factor loadings, intercepts, residual variances of measured subtests, and disturbances of first-order factors of the WISC-IV were generally invariant. Results suggested that WISC-IV index scores and subtests have the same meaning for children in both normative and clinical groups.     

Do personality scale items function differently in people with high and low IQ?

Intelligence differences might contribute to true differences in personality traits. It is also possible that intelligence might contribute to differences in understanding and interpreting personality items. Previous studies have not distinguished clearly between these possibilities. Before it can be accepted that scale score differences actually reflect personality differences, personality items should show measurement invariance. The authors used item response theory to test measurement invariance in the five-factor model scales of the International Personality Item Pool (IPIP) and NEO-Five-Factor Inventory (NEO-FFI) across two groups of participants from the Lothian Birth Cohort 1936 with relatively low and high cognitive abilities. Each group consisted of 320 individuals, with equal numbers of men and women. The mean IQ difference of the groups was 21 points. It was found that the IPIP and NEO-FFI items were measurement invariant across all five scales, making it possible to conclude that any differences in IPIP and NEO-FFI scores between people with low and high cognitive abilities reflected personality trait differences.     

分类数据测量等价性检验方法及其比较：项目阈值(难度)参数的组间差异性检验

测量工具满足等价性是进行多组比较的前提, 测量等价性的检验方法主要有基于CFA的多组比较法和基于IRT的DIF检验两类方法。文章比较了单维测验情境下基于CCFA的DIFFTEST检验方法和基于IRT模型的IRT-LR检验方法, 以及多维测验情境下DIFFTEST和基于MIRT的卡方检验方法的差异。通过模拟研究的方法, 比较了几种方法的检验力和第一类错误, 并考虑了样本总量、样本量的组间均衡性、测验长度、阈值差异大小以及维度间相关程度的影响。研究结果表明：(1)在单维测验下, IRT-LR是比DIFFTEST更为严格的检验方法; 多维测验下, 在测验较长、测验维度之间相关较高时, MIRT-MG比DIFFTEST更容易检验出项目阈值的差异, 而在测验长度较短、维度之间相关较小时, DIFFTEST的检验力反而略高于MIRT-MG方法。(2)随着阈值差值增加, DIFFTEST、IRT-LR和MIRT-MG三种方法的检验力均在增加, 当阈值差异达到中等或较大时, 三种方法都可以有效检验出测验阈值的不等价性。(3)随着样本总量增加, DIFFTEST、IRT-LR和MIRT-MG方法的检验力均在增加; 在总样本量不变, 两组样本均衡情况下三种方法的检验力均高于不均衡的情况。(4)违背等价性题目个数不变时, 测验越长DIFFTEST的检验力会下降, 而IRT-LR和MIRT-MG检验力则上升。(5) DIFFTEST方法的一类错误率平均值接近名义值0.05; 而IRT-LR和MIRT-MG方法的一类错误率平均值远低于0.05。     

The Factor Structure of Effortful Control and Measurement Invariance Across Ethnicity and Sex in a High-Risk Sample

Measurement invariance of a one-factor model of effortful control (EC) was tested for 853 low-income preschoolers (M age = 4.48 years). Using a teacher-report questionnaire and seven behavioral measures, configural invariance (same factor structure across groups), metric invariance (same pattern of factor loadings across groups), and partial scalar invariance (mostly the same intercepts across groups) were established across ethnicity (European Americans, African Americans and Hispanics) and across sex. These results suggest that the latent construct of EC behaved in a similar way across ethnic groups and sex, and that comparisons of mean levels of EC are valid across sex and probably valid across ethnicity, especially when larger numbers of tasks are used. The findings also support the use of diverse behavioral measures as indicators of a single latent EC construct.     

二阶因素模型的测量等价性检验——以大学生网络利他行为量表为例

与一阶因素模型相比,二阶因素模型具有较多优点,但二阶因素模型的测量等价性检验要更复杂,它需要依次进行七个不同水平的检验：形等价、一阶弱等价、二阶弱等价、一阶强等价、二阶强等价、二阶严等价和一阶严等价。低水平的等价性满足之后,才能进行更为严格的高一水平的等价性检验。运用均值和协方差结构（MACS）模型对大学生网络利他行为量表（IABSU）进行二阶因素模型的测量等价性检验,结果表明,IABSU具有跨地域的完全一阶、二阶严等价性。     

Test-Retest Measurement Invariance of Clinic Referred Children’s ADHD Symptoms

This study examined the test-retest measurement invariance of ratings of the ADHD symptoms. Mothers of a group of 217 clinic-referred children (boys?=?169, girls?=?49; age range?=?7 to 17 years) completed ratings of the ADHD symptoms presented in a modified version of the Strengths and Weaknesses of ADHD-Symptoms and Normal Behavior Scale (SWAN-M) twice, 12 months apart. Confirmatory factor analysis (CFA) of their ratings at both time points provided more support for the bifactor model of ADHD [orthogonal general and specific factors for inattention (IA) and hyperactivity/impulsivity (HI) symptoms] over the 2-factor oblique model (factors for inattention IA and HI symptoms). For the bifactor model, measurement invariance testing using multiple-group CFA indicated support for configural and full scalar test-retest invariance when the chi-square difference test was applied. For metric invariance, all but one symptom showed invariance. When the differences in approximate fit indices were applied, there was support for full measurement invariance (configural, metric and scalar). The findings indicate that observed scores (based on maternal ratings of the SWAM-M), twelve months apart, are comparable as they have the same measurement properties. Several practical, theoretical, research and clinical implications of the findings are discussed.     

Statistical power of latent growth curve models to detect quadratic growth

Latent curve models (LCMs) have been used extensively to analyze longitudinal data. However, little is known about the power of LCMs to detect nonlinear trends when they are present in the data. For this study, we utilized simulated data to investigate the power of LCMs to detect the mean of the quadratic slope, Type I error rates, and rates of nonconvergence during the estimation of quadratic LCMs. Five factors were examined: the number of time points, growth magnitude, interindividual variability, sample size, and the R ²s of the measured variables. The results showed that the empirical Type I error rates were close to the nominal value of 5 %. The empirical power to detect the mean of the quadratic slope was affected by the simulation factors. Finally, a substantial proportion of samples failed to converge under conditions of no to small variation in the quadratic factor, small sample sizes, and small R ² of the repeated measures. In general, we recommended that quadratic LCMs be based on samples of (a) at least 250 but ideally 400, when four measurement points are available; (b) at least 100 but ideally 150, when six measurement points are available; (c) at least 50 but ideally 100, when ten measurement points are available.     

Exploring Nonlinear Models in Personality Assessment: Development and Preliminary Validation of a Negative Emotionality Scale

ABSTRACT In this article we discuss the applicability of several new measurement models to the construction of personality scales, and we contrast these models with more traditional approaches in common usage, such as the principal factor analysis model. Our goal is to illustrate how nonlinear item-response models can be profitably used in personality research. We describe the development of a 30-item Negative Emotionality scale that was constructed using nonlinear factor analysis and item-response theory. We also show how traditional (linear) factor analysis can produce misleading results when it is applied to personality items with dichotomous response formats (e.g., true/false, agree/disagree). No formal training in modern measurement theory is assumed of the reader as we describe the nonlinear models that are used in this study in nontechnical language with a minimum of mathematics.     

Measurement invariance of personality traits from a five-factor model perspective: multi-group confirmatory factor analyses of the HP5 inventory

Associations between personality and health may be influenced by contextual factors varying across studied cohorts. Moreover, measurement bias related to contextual factors could also influence these associations. Gender and age have been discussed as important contextual factors when studying personality and health outcomes. An examination of measurement invariance across gender and age may therefore be warranted. In the present study, measurement invariance across age and gender was examined for a five-factor model of personality traits in which scales have been included to operationalise lower-order traits related to health-behaviour or health outcomes. Using multi-group confirmatory factor analysis on a population based cohort (n= 5700), all important parameters of the measurement model were found to be invariant. On the basis of this invariant model, hypotheses of mean differences across age and gender in personality traits were tested. These results were discussed in relation to meta-analyses on personality change and gender differences in personality.     

Assessing relationship quality across cultures: An examination of measurement equivalence

Researchers are increasingly studying close relationships across cultural contexts. One issue that arises when applying scales originally developed in Western countries to a different cultural context is measurement invariance. Researchers often do not examine whether scales show invariance across cultures and thus can be used with confidence. The goal of this article is to discuss the importance of measurement invariance, to discuss what testing invariance involves, and to test the measurement properties of scales of relationship satisfaction, commitment, intimacy, and trust across 4 samples (United States, Canada, Indonesia, and China). Analyses indicated that weak measurement invariance was met for all 4 scales, and assumptions of strong measurement invariance had to be relaxed for only a few items in each scale. Findings are discussed and recommendations are made regarding using these or other scales that have been shown to meet assumptions of invariance across different cultural groups.     

Measurement invariance of the appearance schemas inventory-revised and the body image quality of life inventory across age and gender

The majority of body image measures have largely been developed with younger female samples. Before these measures can be applied to men, and to middle-aged and older women, and used to make gender and age comparisons, they must exhibit adequate cross-group measurement invariance. This study examined the age and gender cross-group measurement invariance of the Appearance Schemas Inventory-Revised (ASI-R) and the Body Image Quality of Life Inventory (BIQLI), with a sample of 1,262 adults (422 men and 840 women) aged 18 to 98 years. For the ASI-R, all groups met requirements for configural and metric invariance. Scalar invariance was found only for the three age groups, which indicated that mean comparisons may be conducted across gender for young, middle-aged, and older adults but should not be conducted across age groups within either gender. Results for the BIQLI indicated that observed mean comparisons may be conducted across all age and gender groups.     

Distinguishing Between Latent Classes and Continuous Factors with Categorical Outcomes: Class Invariance of Parameters of Factor Mixture Models

Factor mixture models are latent variable models with categorical and continuous latent variables that can be used as a model-based approach to clustering. A previous article covered the results of a simulation study showing that in the absence of model violations, it is usually possible to choose the correct model when fitting a series of models with different numbers of classes and factors within class. The response format in the first study was limited to normally distributed outcomes. This article has 2 main goals, first, to replicate parts of the first study with 5-point Likert scale and binary outcomes, and second, to address the issue of testing class invariance of thresholds and loadings. Testing for class invariance of parameters is important in the context of measurement invariance and when using mixture models to approximate nonnormal distributions. Results show that it is possible to discriminate between latent class models and factor models even if responses are categorical. Comparing models with and without class-specific parameters can lead to incorrectly accepting parameter invariance if the compared models differ substantially with respect to the number of estimated parameters. The simulation study is complemented with an illustration of a factor mixture analysis of 10 binary depression items obtained from a female subsample of the Virginia Twin Registry.