Deflation-Corrected Estimators of Reliability

Underestimation of reliability is discussed from the viewpoint of deflation in estimates of reliability caused by artificial systematic technical or mechanical error in the estimates of correlation (MEC). Most traditional estimators of reliability embed product–moment correlation coefficient (PMC) in the form of item–score correlation (Rit) or principal component or factor loading (λi). PMC is known to be severely affected by several sources of deflation such as the difficulty level of the item and discrepancy of the scales of the variables of interest and, hence, the estimates by Rit and λi are always deflated in the settings related to estimating reliability. As a short-cut to deflation-corrected estimators of reliability, this article suggests a procedure where Rit and λi in the estimators of reliability are replaced by alternative estimators of correlation that are less deflated. These estimators are called deflation-corrected estimators of correlation (DCER). Several families of DCERs are proposed and their behavior is studied by using polychoric correlation coefficient, Goodman–Kruskal gamma, and Somers delta as examples of MEC-corrected coefficients of correlation.

Bivariate Distributions Underlying Responses to Ordinal Variables

The association between two ordinal variables can be expressed with a polychoric correlation coefficient. This coefficient is conventionally based on the assumption that responses to ordinal variables are generated by two underlying continuous latent variables with a bivariate normal distribution. When the underlying bivariate normality assumption is violated, the estimated polychoric correlation coefficient may be biased. In such a case, we may consider other distributions. In this paper, we aimed to provide an illustration of fitting various bivariate distributions to empirical ordinal data and examining how estimates of the polychoric correlation may vary under different distributional assumptions. Results suggested that the bivariate normal and skew-normal distributions rarely hold in the empirical datasets. In contrast, mixtures of bivariate normal distributions were often not rejected.

Please avoid the standardized alpha and the ordinal alpha

Coefficient alpha is the most widely used measure of reliability. A cousin of coefficient alpha is the standardized alpha, which is calculated from the correlation matrix instead of the covariance matrix. This paper makes the case that standardized alpha should never be used. It is worse than coefficient alpha as an estimator of the congeneric reliability, there are superior estimators of the standardized reliability, and standardization should be avoided to begin with. Ordinal alpha, the standardized alpha based on the polychoric correlation matrix, should also be avoided, as it has no concrete interpretation. We propose a concrete variant of the ordinal alpha and show how its related to the ordinal alpha.

Construct validity of Rosenberg Self-esteem Scale in Brazilian Athletic Context

Objective: The purpose of this study was to evaluate the psychometric properties of the Rosenberg Self-esteem Scale in the athletic context of Brazil. Method: In total, 387 athletes participated in the study, 232 men and 155 women, with a mean age of 22.1+/-4.5 years, practitioners of team modalities in clubs in Southern Brazil. The construct validity was evaluated through exploratory Factorial Analyses with Oblimin Rotation and the factorial weight 0.3 was used to exclude items. Cronbach’s Alpha and Polychoric Correlation evaluated the internal variance consistency. Results: The Rosenberg Self-esteem Scale uploaded on 2 factors showed 61% of the variance of the construct, with factor 1 adding items about positive self-esteem and factor 2 about negative self-esteem. To confirm the internal consistency of the instrument, we performed polychoric correlation between the items on the scale. All items showed significant positive correlation above 0.3 (p>0.05) confirming the good internal consistency of the questionnaire. Conclusion: This research identifies good psychometric properties of the Rosenberg Self-esteem Scale in the Brazilian sport context of athletes of team sports. The bifactorial structure was verified, agreeing with the original proposal, suggesting the separate score calculation of each factor on the self-esteem Scale.

Czech Version of the Spiritual Well-Being Scale: Evaluation and Psychometric Properties

Spirituality and spiritual well-being are connected with many areas of human life. Thus, especially in secular countries, there is a need for reliable validated instruments for measuring spirituality. The Spiritual Well-Being Scale is among the world’s most often used tools; therefore, the aim of this study was its psychometrical evaluation in the secular environment of the Czech Republic on a nationally representative sample (n = 1797, mean age: 45.9 ± 17.67; 48.6% men). A non-parametric comparison of different sociodemographic groups showed a higher disposition for experiencing spirituality among women, older people, and divorced persons. Based on confirmatory factor analysis, negatively worded items were excluded using a polychoric correlation matrix. The new version of the scale consisting of 11 items had good internal consistency (Cronbach’s α = 0.85; McDonald’s ωt = 0.91). The two-factor model of this shortened version, with factors corresponding to the Religious and the Existential subscales of the Spiritual Well-Being Scale, shows a satisfactory fit with the data, where the loadings of all items ranged from medium to high. Thus, this study offered a new version of the tool, convenient for measuring spiritual well-being in secular conditions.

Construct validity of the Brazilian version of the Medical Outcomes Study Social Support Survey (MOS-SSS) in a sample of elderly users of the primary healthcare system

Objective To assess the psychometric properties of the Medical Outcomes Study Social Support Survey (MOS-SSS) considering a sample of elderly users of the primary healthcare facilities of Ribeirão Preto, state of São Paulo, southeast Brazil. Methods The MOS-SSS is a widely used measurement of social support in different contexts, consisting of 19 items with answer categories that range on a 7-point rating scale. Data collection regarding the psychometric properties of the MOS-SSS was performed in a stratified sample of elderly users of primary healthcare facilities of Ribeirão Preto. Data were collected at five district basic health units located in the city through face-to-face interviews. Polychoric correlation matrix and exploratory (EFA) and confirmatory (CFA) factor analyses were performed. Results A total of 357 elderly subjects aged 60 years or older participated in the study (62.7% females). According to the polychoric correlation matrix, higher coefficients of correlation (> 0.90) were detected among 12 pairs of items and grouped into four factors, as suggested for EFA. The results of the CFA confirmed the construct validity of the four-factor structure of the MOS-SSS when applied to our sample, as well as the stability of this model in distinct subsamples. Conclusion The four-factor structure of the MOS-SSS was found to be suitable and presented adequate construct validity for the assessment of social support in elderly users of primary healthcare facilities.

Mind the parent-adolescent gap: A comparison of parents’ and adolescents’ assessments of their relationship and discussions about sex

Purpose: To compare parent and child reports on their relationship and communication about sex; quantify agreement; and find characteristics associated with higher agreement.Methods: Data is baseline data from an evaluation of Talking Parents, Healthy Teens, a multi-session worksite-based parenting program. Participants are 569 parents of 6-10th grades who responded to an advertisement posted in their workplace, and their 6-10th grade children (n=683): 683 parent-child dyads. Self-administered survey data were collected in Southern California from 2002-2004. We compare parent and child responses to 68 items about their relationships and communication about sex, and computed polychoric correlation (PCC), an agreement measure that corrects for possible parent-child differences in response threshholds, across dyads and across items. Factors associated with higher agreement were found through bivariate comparison of PCC; linear regression on intra-dyad PCC; and linear regression on raw bias.Results: After adjusting for possible parent-child differences in response threshholds, PCC for items were low, with median 0.34 (inter-quartile range (IQR) (0.22, 0.41)). Agreement was higher for sexual discussion topics (median 0.41 (IQR (0.37, 0.46))) than other items (Wilcoxon p<0.001); in general, agreement was higher for factual than emotionally negative or hypothetical items. PCC for dyads was very high, with median 0.87 (IQR (0.84, 0.91)), but left-skewed (skewness = -3.1). Factors associated with greater parent-child agreement include younger child age, better parenting skills, parent married or living as married, and parent recollection of good communication with their own parents. Agreement was not associated with socioeconomic factors.Conclusions: Survey-response discordance appears not to be solely attributable to response bias. Items about concrete events yield better agreement than hypothetical items. Response discordance may be partially attributable to different parent and child perceptions of their relationship because less discordance is evidence among parents with good parenting skills or who recall good communication with their own parents.