On structural equation modeling with data that are not missing completely at random

A general latent variable model is given which includes the specification of a missing data mechanism. This framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data. Here, missing completely at random is not a prerequisite for unbiased estimation in large samples, as when using the traditional listwise or pairwise present data approaches. The theory is connected with old and new results in the area of selection and factorial invariance. It is pointed out that in many applications, maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software, such as LISREL and LISCOMP. Several sets of artifical data are generated within the general model framework. The proposed estimator is compared to the two traditional ones and found superior.The research of the first author was supported by grant No. SES-8312583 from the National Science Foundation and by a Spencer Foundation grant. We wish to thank Chuen-Rong Chan for drawing the path diagram.     

Some properties of estimated scale invariant covariance structures

Scale invariance is a property shared by many covariance structure models employed in practice. An example is provided by the well-known LISREL model subject only to classical normalizations and zero constraints on the parameters. It is shown that scale invariance implies that the estimated covariannce matrix must satisfy certain equations, and the nature of these equations depends on the fitting function used. In this context, the paper considers two classes of fitting functions: weighted least squares and the class of functions proposed by Swain.Constructive comments by the referees are greatly appreciated. The author gratefully acknowledges Michael Browne's interest in his work.     

Probability of directional errors with disordinal (qualitative) interaction

In a factorial design with two or more factors, there is nonzero interaction when the differences among the levels of one factor vary with levels of other factors. The interaction is disordinal or qualitative with respect to a specific factor, sayA, if the difference between at least two levels ofA is positive for some and negative for some levels of the other factors. Using standard methods of analysis, there is a potentially large probability of drawing incorrect conclusions about the signs of differences in the presence of disordinal interaction. The maximum probability of such incorrect conclusions, or directional errors, is derived for two-factor designs in which the factor of interest has two levels and the number of levels of the other factor varies.     

Comparing Chinese youth with American youth on adjustment: An illustration of measurement issues in cross-cultural research

In this article, we used results from two studies to show the need to go beyond linguistic equivalence to establish construct validity and measurement invariance in cross-cultural research. Study 1 examined Rosenberg Self-Esteem (RSE; 10 items) data from 156 Mainland Chinese youth (M = 13.8 years, SD = .53) and 213 Chinese-American youth (M = 13.6 years, SD = 2.1) from high socioeconomic status (SES) families. The Chinese translation of the RSE has been widely used. Study 2 included 1060 Mainland Chinese youth (M = 15.6 years, SD = 2.3) and 412 racially diverse American youth (M = 16.0, SD = 2.9) from all SES backgrounds. Data were collected with the third and newest edition of the Behavioural Assessment System for Children-Self Report of Personality (BASC-3-SRP; 189 items). We translated and back-translated the BASC-3-SRP between English and Chinese to establish linguistic equivalence. All participants were females. Study 1 showed that the RSE had acceptable internal consistency but lacked construct validity. Study 2 showed that the original and the translated BASC-3-SRP had good internal consistency and construct validity, but nine of its 16 subscales lacked measurement invariance. These results highlight measurement issues facing international and cross-cultural research.     

Factorial validation and measurement invariance of the French version of the multidimensional competitive orientation inventory (FVMCOI) in the sport field

IntroductionLittle is known about the importance of the adaptive, maladaptive and neutral facets of competitive orientations among French athletes.ObjectiveThe aim of this study is to test the factorial validation and measurement invariance of the French version of the multidimensional competitive orientation inventory (FVMCOI) from the original version (MCOI, Orosz et al., 2018), which included 12 items and four factors (i.e., hypercompetitive orientation, self-developmental competitive orientation, anxiety-driven competition avoidance, and lack of interest toward competition).MethodA series of three complementary studies was carried out with a total sample of 891 competitors.ResultsFollowing cross-cultural validation methods a preliminary version of the FVMCOI was constructed and the clarity of its items was established (study 1). Then, exploratory structural equation modeling (ESEM) confirmed that the four-factor model for the FVMCOI was factorially valid, and consistent with the model of the original version. As such, the multiple-group invariance tests showed that the FVMCOI was partially invariant across both age and gender and fully invariant across type of sport, level of competition and over time (study 2). Finally, the concurrent validity of the FVMCOI was demonstrated through its expected relationships with achievement goals, competitive aggressiveness and anger in sport (study 3).ConclusionThe establishment of the FVMCOI extends the research in sport psychology by allowing an extensive psychometric study of the MCOI in the sport domain and providing deeper insights into the healthy, unhealthy, and neutral nature of competitive orientation in this context. The FVMCOI's potential practical applications in sport context, with some limitations and perspectives of this study, are also discussed.     

Modeling the Influence of Language Input Statistics on Children's Speech Production

We trained a computational model (the Chunk-Based Learner; CBL) on a longitudinal corpus of child–caregiver interactions in English to test whether one proposed statistical learning mechanism—backward transitional probability—is able to predict children's speech productions with stable accuracy throughout the first few years of development. We predicted that the model less accurately reconstructs children's speech productions as they grow older because children gradually begin to generate speech using abstracted forms rather than specific “chunks” from their speech environment. To test this idea, we trained the model on both recently encountered and cumulative speech input from a longitudinal child language corpus. We then assessed whether the model could accurately reconstruct children's speech. Controlling for utterance length and the presence of duplicate chunks, we found no evidence that the CBL becomes less accurate in its ability to reconstruct children's speech with age.     

Measurement invariance and age-related differences of trait anger across the adult lifespan

The present study examined measurement invariance of trait anger with respect to age. In addition, age-related differences in latent variables (factor variances, factor covariances, and factor means) were investigated. A sample of 1216 participants, divided into six age groups, ranging from under 30 to over 70 years, was tested using the angry temperament and angry reaction scales from the State-Trait Anger Expression Inventory (STAXI; Spielberger, 1988). Results show that strong measurement invariance held across the six age groups. For both angry temperament and angry reaction, factor variances tended to decrease into middle age and then increase again into old age. Factor correlations decreased into old age, implying a differentiation of trait anger. Finally, regarding factor means, older adults showed less anger than younger adults, suggesting higher levels of self-regulation or less exposure to anger-provoking contexts in later life.     

Cross-cultural validation of the positivity-scale in five European countries

The aim of the present paper was to test the cross-cultural validity of the Positivity-Scale (P-Scale), a new questionnaire designed for the measurement of positivity (i.e., general tendency to evaluate self, life, and future in a positive way). Participants (N = 3544) from Italy, Germany, Spain, Poland, and Serbia answered eight items of the P-Scale and responded to items from other well-validated measures. Confirmatory Factor Analysis supported the assumed one-factor structure of the P-Scale and demonstrated its gender invariance in each country and cross-cultural validity. Correlation analyses revealed significant and positive associations of the P-Scale with self-esteem, life satisfaction, optimism, and a latent factor variable of positivity, and a negative relation to depression. The findings provided support for the convergent validity of the P-Scale across countries. Possible applications of the P-Scale are suggested. Implications for further research on conditions and outcomes of positivity in different cultural contexts are discussed.     

Consequences of Ignoring Guessing Effects on Measurement Invariance Analysis

Pseudo-guessing parameters are present in item response theory applications for many educational assessments. When sample size is not sufficiently large, the guessing parameters may be ignored from the analysis. This study examines the impact of ignoring pseudo-guessing parameters on measurement invariance analysis, specifically, on item difficulty, item discrimination, and mean and variance of ability distribution. Results show that when non-zero guessing parameters are ignored from the measurement invariance analysis, item discrimination estimates tend to decrease particularly for more difficult items, and item difficulty estimates decrease unless the items are highly discriminating and difficult. As the guessing parameter increases, the size of the decrease in item discrimination and difficulty tends to increase, and the estimated mean and variance of ability distribution tend to be inaccurate. When two groups have heterogeneous ability distributions, ignoring the guessing parameter affects the reference group and the focal group differently. Implications of result findings are discussed.     

Are there gender differences in cognitive reflection? Invariance and differences related to mathematics

ABSTRACT

Cognitive reflection is recognized as an important skill, which is necessary for making advantageous decisions. Even though gender differences in the Cognitive Reflection test (CRT) appear to be robust across multiple studies, little research has examined the source of the gender gap in performance. In Study 1, we tested the invariance of the scale across genders. In Study 2, we investigated the role of math anxiety, mathematical reasoning, and gender in CRT performance. The results attested the measurement equivalence of the Cognitive Reflection Test – Long (CRT- L), when administered to male and female students. Additionally, the results of the mediation analysis showed an indirect effect of gender on CRT-L performance through mathematical reasoning and math anxiety. The direct effect of gender was no longer statistically significant after accounting for the other variables. The current findings suggest that cognitive reflection is affected by numerical skills and related feelings.