Effects of varying numbers of Likert scale points on factor structure of the Rosenberg Self‐Esteem Scale

Likert‐type rating scales are among the most widely used tools in psychological research. Different numbers of response categories would likely affect response style, data distribution, reliability, and construct validity. There is a lack of research in factor structure invariance under Likert scales with different numbers of categories. The purpose of this study is to examine the effects of varying numbers of Likert points (4–11) on scale properties such as factor structure, external validity, and latent means based on the Rosenberg Self‐Esteem Scale (M. Rosenberg, 1989 ). The sample consists of 1,807 students from secondary schools in Macau. Confirmatory factor analysis shows that the correlated two‐factor model is the most appropriate one; longitudinal invariance analysis reveals that measurement invariance across Likert scales was satisfied at the scalar level. In addition, latent mean scores on the two factors as well as observed means on the subscales are comparable across Likert scales. Moreover, the measurement model across Likert scales exhibit similar external validity. Although psychometric properties are mostly similar among a different number of points, the 4‐point Likert scale is not recommended for its higher skewness and lower loadings; the 11‐point Likert scale from 0 to 10 is slightly preferred for its higher loadings and composite reliability.     

Exploring a Source of Uneven Score Equity across the Test Score Range

Score equity assessment (SEA) refers to an examination of population invariance of equating across two or more subpopulations of test examinees. Previous SEA studies have shown that score equity may be present for examinees scoring at particular test score ranges but absent for examinees scoring at other score ranges. No studies to date have performed research for the purpose of understanding why score equity can be inconsistent across the score range of some tests. The purpose of this study is to explore a source of uneven subpopulation score equity across the score range of a test. It is hypothesized that the difficulty of anchor items displaying differential item functioning (DIF) is directly related to the score location at which issues of score inequity are observed. The simulation study supports the hypothesis that the difficulty of DIF items has a systematic impact on the uneven nature of conditional score equity.     

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。     

Measurement invariance,factor analysis and factorial invariance

Several concepts are introduced and defined: measurement invariance, structural bias, weak measurement invariance, strong factorial invariance, and strict factorial invariance. It is shown that factorial invariance has implications for (weak) measurement invariance. Definitions of fairness in employment/admissions testing and salary equity are provided and it is argued that strict factorial invariance is required for fairness/equity to exist. Implications for item and test bias are developed and it is argued that item or test bias probably depends on the existence of latent variables that are irrelevant to the primary goal of test constructers.Presidential address delivered at the Annual Meeting of the Psychometric Society in Berkeley, California, June 18–20, 1993.     

Local homogeneity in latent trait models. A characterization of the homogeneous monotone irt model

The stochastic subject formulation of latent trait models contends that, within a given subject, the event of obtaining a certain response pattern may be probabilistic. Ordinary latent trait models do not imply that these within-subject probabilities are identical to the conditional probabilities specified by the model. The latter condition is called local homogeneity. It is shown that local homgeneity is equivalent to subpopulation invariance of the model. In case of the monotone IRT model, local homogeneity implies absence of item bias, absence of item specific traits, and the possibility to join overlapping subtests. The following characterization theorem is proved: the homogeneous monotone IRT model holds for a finite or countable item pool if and only if the pool is experimentally independent and pairwise nonnegative association holds in every positive subpopulation.This research was supported by the Dutch Interuniversity Graduate School of Psychometrics and Sociometrics. The authors wish to thank two reviewers for their thorough comments.     

RELIGIOUS AND MYSTICAL STATES: A NEUROPSYCHOLOGICAL MODEL

Abstract. This paper first considers the current confusion in categorizing and even describing mystical states, including experiences of God, the Void, and lesser religious experiences. The paper presents the necessity of studying the neuropsychological substrate of such experiences both to understand them in greater depth and to help resolve scholarly confusion in this area. As a prelude to presenting a neuropsychological model, the basic principles of brain organization are reviewed, including hemispheri-city; primary, secondary, and tertiary sensory receptive areas; their motor analogues; prefrontosensorial polarity; and the integration of limbic functioning into cortical activity. A neuropsychological model for mystical states is then presented in terms of differential stimulation and deafferentation of various tertiary sensory association areas, along with integration of various patterns of limbic stimulation.     

Substitutability between conditioned and primary reinforcers in discrimination acquisition.

Rats and pigeons were trained on a series of reversals of a conditional simultaneous discrimination. The percentage of reinforcement for correct trials was varied across reversals. When nonreinforced correct trials produced the same feedback as incorrect trials, the number of errors to reach an acquisition criterion was greater for smaller percentages of reinforcement, but the number of reinforcers required was either approximately constant or smaller for the smaller percentages. When a stimulus paired with food (the conditioned reinforcer) was added on nonreinforced correct trials, both measures were substantially decreased. When the same stimulus was presented, but without a history of food pairing, learning rate was similar to when no stimulus was presented on nonreinforced trials. The results provide direct evidence that conditioned reinforcers may substitute, although imperfectly, for a primary reinforcer, and that pairing with the primary reinforcer is a necessary condition for such substitutability to occur.     

Factor structure and measurement invariance of the multidimensional driving style inventory across gender and age: An ESEM approach

The Multidimensional Driving Style Inventory (MDSI) is the most comprehensive measure of typical driving behavior to date and has been frequently used to compare driving styles across different groups of drivers, particularly between gender- and age-related groups. However, the factor structure of MDSI has not been clearly established and its measurement invariance has not been demonstrated. The goal of the present study was to examine the internal structure and measurement invariance of the MDSI across gender and age. A sample of 1277 drivers from Argentina responded to the Argentinian version of the MDSI. Exploratory structural equation modeling (ESEM) was used to test the factor structure and measurement invariance across females (n = 602) and males (n = 675), and across young (18–29, n = 558), adult (30–49, n = 395) and older (50 and older, n = 317) drivers. The results showed that a 36-item six-factor ESEM model represented by risky, angry, dissociative, anxious, distress-reduction and careful and patient driving styles was the best model based on fit indices and interpretability. Configural, weak and strong invariance of the six-factor ESEM model across gender and age was also supported. The MDSI in its Argentinian version is equivalent across gender and age, supporting the validity of previous research findings examining gender and age differences in driving styles. Future studies should examine the measurement invariance of the MDSI across other relevant driving-related variables.     

等效性检验——结构方程模型评价和测量不变性分析的新视角

常用的结构方程模型拟合指数存在一定局限, 如χ ²以传统零假设为目标假设, 无法验证模型, 而RMSEA和CFI等描述性的拟合指数不具备推断统计性质, 等效性检验有效弥补了这些问题。首先说明等效性检验如何评价单个模型的拟合, 并解释其与零假设检验的不同, 然后介绍等效性检验如何分析测量不变性, 接着用实证数据展示了等效性检验在单个模型评价和测量不变性检验中的效果, 并与传统模型评价方法比较。     

Testing Measurement Invariance of the Dark Triad Dirty Dozen in a Belgian Adult Sample

The Dirty Dozen (Jonason & Webster, 2010) is a frequently used concise version of the Dark Triad to measure three socially aversive personality traits: Machiavellianism, psychopathy and, narcissism. The present study has examined measurement invariance in a sample of Belgian adults. The present study aims to assess measurement invariance of the Dutch version of the Dirty Dozen measure across gender in a large city-based representative adult sample in Belgium (N = 1587). Multi-group first-order confirmatory factor analysis for categorical indicators was utilized. In addition, unique associations between Dirty Dozen traits, trait self-control and, acceptance of illegitimate norms were examined in a series of structural equation models. Results indicated that the internal consistency of the Dirty Dozen subscales was good for Machiavellianism (α = 0.80) and narcissism (α = 0.80), but modest for psychopathy (α = 0.64). The hypothesized three correlated factors model with separate factors for Machiavellianism, psychopathy and, narcissism provided a poor fit for men and women. Invariance testing across gender showed evidence for weak invariance only, indicating that the underlying latent factors are measured the same way with the same metric in the two populations. However, we were not able to establish strong measurement invariance. Observed group differences should be interpreted with caution. Furthermore, Machiavellianism and psychopathy were strongly associated with trait self-control in both men and women. Strong correlations were found between acceptance of illegitimate norms and Dirty Dozen traits, Machiavellianism and, psychopathy, but not with narcissism.