Sample size and bentler and Bonett's nonnormed fit index

Bentler and Bonett's nonnormed fit index is a widely used measure of goodness of fit for the analysis of covariance structures. This note shows that contrary to what has been claimed the nonnormed fit index is dependent on sample size. Specifically for a constant value of a fitting function, the nonnormed index is inversely related to sample size. A simple alternative fit measure is proposed that removes this dependency. In addition, it is shown that this new measure as well as the old nonnormed fit index can be applied to any fitting function that measures the deviation of the observed covariance matrix from the covariance matrix implied by the parameter estimates for a model.     

The many null distributions of person fit indices

This paper deals with the situation of an investigator who has collected the scores ofn persons to a set ofk dichotomous items, and wants to investigate whether the answers of all respondents are compatible with the one parameter logistic test model of Rasch. Contrary to the standard analysis of the Rasch model, where all persons are kept in the analysis and badly fittingitems may be removed, this paper studies the alternative model in which a small minority ofpersons has an answer strategy not described by the Rasch model. Such persons are called anomalous or aberrant. From the response vectors consisting ofk symbols each equal to 0 or 1, it is desired to classify each respondent as either anomalous or as conforming to the model. As this model is probabilistic, such a classification will possibly involve false positives and false negatives. Both for the Rasch model and for other item response models, the literature contains several proposals for a person fit index, which expresses for each individual the plausibility that his/her behavior follows the model. The present paper argues that such indices can only provide a satisfactory solution to the classification problem if their statistical distribution is known under the null hypothesis that all persons answer according to the model. This distribution, however, turns out to be rather different for different values of the person's latent trait value. This value will be called ability parameter, although our results are equally valid for Rasch scales measuring other attributes.As the true ability parameter is unknown, one can only use its estimate in order to obtain an estimated person fit value and an estimated null hypothesis distribution. The paper describes three specifications for the latter: assuming that the true ability equals its estimate, integrating across the ability distribution assumed for the population, and conditioning on the total score, which is in the Rasch model the sufficient statistic for the ability parameter.Classification rules for aberrance will be worked out for each of the three specifications. Depending on test length, item parameters and desired accuracy, they are based on the exact distribution, its Monte Carlo estimate and a new and promising approximation based on the moments of the person fit statistic. Results for the likelihood person fit statistic are given in detail, the methods could also be applied to other fit statistics. A comparison of the three specifications results in the recommendation to condition on the total score, as this avoids some problems of interpretation that affect the other two specifications.The authors express their gratitude to the reviewers and to many colleagues for comments on an earlier version.     

A note on the factor analysis of partial covariance matrices

A relationship is given between the joint common factor structure of two sets of variables, and the factor structure of the partial covariance matrix of one of the sets with the other partialled out.     

Likelihood methods for testing group problem solving models with censored data

Problem solving models relating individual and group solution times under time limit censoring are presented. Maximum likelihood estimates of parameters of the resulting censored distributions are derived and goodness of fit tests for the individual-group models are constructed. The methods are illustrated on data previously analyzed by Restle and Davis.This research was supported by grants from the Graduate School, University of Minnesota. Also, work of the second author was aided by a Single Quarter Leave granted by the Regents of the University of Minnesota.     

Applying the Bradley-Terry-Luce method to P-E fit

This study attempted to increase the size of the correlation between person-environment (P-E) fit and job satisfaction by rescaling the instrumentation of the Theory of Work Adjustment using the Bradley-Terry-Luce method and a probability-based fit index. This approach worked as well as, but failed to outperform, the currently used correlation-based fit index. However, a probability-based fit index offers the advantage of being intuitively easier to understand than a correlation-based index. The very high correlation between the correlation-based fit index and the probability-based fit index suggests that both assess the same construct. It is argued that, considering the restriction of range common to all assessments of job satisfaction, the correlation between fit index and job satisfaction may not represent an upper limit, but rather a lower bound of the relationship between P-E fit and job satisfaction.     

A Goodness-of-Fit Approach to Informed Consent for Pediatric Intervention Research

As children and adolescents receive increased research attention, ethical issues related to obtaining informed consent for pediatric intervention research have come into greater focus. In this article, we conceptualize parent permission and child assent within a goodness-of-fit framework that encourages investigators to create consent procedures “fitted” to the research context, the child's cognitive and emotional maturity, and the family system. Drawing on relevant literature and a hypothetical case example, we highlight four factors investigators may consider when constructing consent procedures that best reflect participants' rights, concerns, and well-being: (a) the child's current assent capacity and the likely impact of study information on the child's mental and physical development, (b) parents' understanding of their child's treatment needs and distinctions between treatment and clinical trials research, (c) the family's history of shared decision making, and (d) the child's strivings for autonomy within the context of their parents' duty to make decisions in the child's best interest.     

A quantitative review of the relationship between person-organization fit and behavioral outcomes

This paper extends the meta-analysis of Verquer, Beehr, and Wagner by providing a meta-analytic review of the relationship between person-organization fit (PO fit) and behavioral criteria (job performance, organizational citizenship behaviors, and turnover). Results indicate that PO fit is weakly to moderately related to each of these outcome variables. Results further show that the way in which fit is measured is an important moderator of fit-outcome relationships; however, definition of fit did not moderate the relationship between fit and behavioral criterion. Implications of these findings and avenues for future research are discussed.     

A gender perspective on Person-Manager fit and managerial advancement

This article presents two studies examining (1) the relationship between Person-Manager (P-M) fit and managerial advancement of women and men with, and without managerial aspirations and (2) the P-M fit as related to managerial and non-managerial women. The P-M fit was assessed by computing the congruence between participants' self-rated personality profile and the perceived personality profile of a manager. Sex (men show a higher P-M fit than women), gender (the higher the individual's masculine gender-role, the higher the P-M fit) and group (managers and managerial aspirants show a higher P-M fit than non-managerial aspirants and non-managers) hypotheses were tested. There was no support for the sex difference hypothesis. However, the group and gender hypotheses were confirmed showing that managers and managerial aspirants had a higher P-M fit than non-managers and non-aspirants. Further, analyses revealed that the higher the participants' masculinity scores, the higher the P-M fit. Implications of these findings are discussed in relation to the gendered image of the managerial role and adaptation theory.     

Paired comparisons with individual differences

A model of Bradley-Terry type for paired comparisons is considered. In addition to the usual parameters, the model allows for individual parameters and corresponding parameters for the choice-alternatives. The model is applied to a set of data from a Danish investigation of the attitude of blue collar workers towards alternative social gains. The proposed model is finally compared to a model recently suggested by Schönemann and Wang.     

A still further note on freeman's measure of association

This article demonstrates that Freeman's theta, a measure of association between a nominal variable and an ordinal variable, has a sampling distribution identical with the sampling distribution of Mann-Whitney'sU.     

Relationships between various person–environment fit types and employee withdrawal behavior: A longitudinal study

This study investigated the relationships between various person–environment fit types and employees' withdrawal attitudes and behaviors. I collected an initial survey data from 901 employees who had been with their organizations for 6 months at most and whose current organizations were their first employers. Of these respondents, only 297 responded to the second survey, 6 months after the first. The results showed person–job, person–supervisor, and person–organization fits correlated significantly with turnover intention on the first survey. Logistic regression analyses showed only person–organization fit correlated significantly with actual turnover at the time of Survey 2. I discuss implications and limitations of this study.     

Linking the fits, fitting the links: Connecting different types of PO fit to attitudinal outcomes

In this paper we explore the linkages among various types of person-organization (PO) fit and their effects on employee attitudinal outcomes. We propose and test a conceptual model which links various types of fits—objective fit, perceived fit and subjective fit—in a hierarchical order of cognitive information processing and relate them to employee organizational commitment and job satisfaction. By unveiling how the different types of fit relate to each other in influencing individual outcomes, we address some of the theoretical and methodological concerns in the use of different methods in measuring PO fit.     

Relation of person-environment fit to career certainty

This study examined the person-environment fit-career outcome relation by observing interests, self-efficacy and parental support as person aspects and major and occupational choice as separate indicators of the environment. Career certainty was selected as a career outcome. Two dimensional fit indices (People-Things and Data-Ideas) were examined as was the incremental validity of adding prestige fit indices. In addition, we examined the moderation of these PE fit-outcome relations by ethnicity (Anglos vs. Latino/a’s). Results revealed that the PE fit predictors were moderately related and none of the two dimensional PE fit predictors significantly related to career certainty, while nearly all of the Prestige PE fit-certainty relations were significant. Support was found for the spherical structure of work types and person variables [Tracey, T. J. G., & Rounds, J. (1996b). Contributions of the spherical representation of vocational interests. Journal of Vocational Behavior, 48, 85-95].     

The effects of managerial regulatory fit priming on reactions to explanations

We investigated the interactive effects of regulatory focus priming and message framing on the perceived fairness of unfavorable events. We hypothesized that individuals’ perceptions of fairness are higher when they receive a regulatory focus prime (promotion versus prevention) that is congruent with the framing of an explanation (gain versus loss), as opposed to one that is incongruent. We also hypothesized that these effects are mediated by counterfactual thinking. Three studies revealed that primed regulatory fit (promotion/gain or prevention/loss) led to higher levels of justice perceptions than regulatory misfit (promotion/loss or prevention/gain). Additionally, “could” and “should” counterfactuals partially mediated the relationship between regulatory fit and interactional justice (Study 3).     

Disease controllability moderates the effect of coping efficacy on positive affect

Objective: This study aims to test experimentally whether coping strategies (approach- vs. avoidance-oriented coping) have differential effects under conditions of high or low stressor controllability.

Design: Undergraduates (62 women, 30 men) participated in a 2 × 2 experimental study where they were introduced to a fictitious disease (tisomerase enzyme deficiency) said to be either controllable or uncontrollable and an approach- or avoidance-oriented coping behaviour induction.

Main Outcome Measures: Changes in positive and negative affect.

Results: A significant disease control x coping interaction on positive affect (f² = .07, p = .011) revealed that approach-coping condition participants had higher positive affect than avoidance-coping condition participants when disease control was high (d = .94, p = .003), but not when it was low (d = .11, p = .93). The experimental conditions did not significantly influence negative affect.

Conclusion: Results demonstrate that disease control moderates the salubrious effects of approach-oriented coping on positive affect. For controllable, but not uncontrollable, health stressors, promoting problem-focused approach-oriented coping strategies may be recommended.     

A further note on freeman's measure of association

This note extends and elaborates Hubert's attempt to provide an interpretation of Freeman's measure of association,. The measure is used in a a contingency table when observations are ordered on one variable and unordered on the other. No attempt is made explore the distribution of.     

The relation between career decision-making strategies and person-job fit: A study of job changers

This study examined relations between three career decision-making strategies (rational, intuitive, and dependent) and person-job fit among 361 professionals who had recently changed jobs. We found that the relation between each decision-making strategy and fit was contingent upon the concurrent use of other strategies. A rational strategy related more strongly to fit when individuals also engaged in extensive intuitive decision making than when they engaged in limited intuitive decision making. In addition, a dependent strategy related negatively to fit only in the absence of extensive rational or intuitive strategies. Moreover, self-awareness and awareness of the environment mediated relations between career decision-making strategies and person-job fit. The implications of these findings for future research on career decision making were discussed.