Goodness-of-Fit Tests and Model Validity (Statistics for Industry and Technology)

Goodness-of-Fit Tests and Model Validity

The psychometric properties of the questionnaire were initially investigated in two different studies Luthans, Avolio et al. The goodness of fit indices obtained in the confirmatory factor analyses applied in both studies provided evidence for the second-order model with four first-order dimensions. In addition, the data from the regression analyses in study two confirmed the hypothesis that psychological capital is a better predictor of satisfaction and work performance when compared to each of its four components.

Avey interpreted these results, in combination with the results of a greater predictive power of the general factor over its components Luthans, Avolio et al. Nevertheless, other studies developed with the PCQ did not provide evidence in favor of the theoretical model that supported the development of the instrument. The short version of the Psychological Capital Questionnaire PCQ consists of 12 items taken from the full version, which are also distributed among four subscales: One of the first studies to use this version was developed in China by Luthans Avey, Clapp-Smith and Li , although the authors did not test its structure and only calculated the precision of the total score 0.

The same happened in a subsequent study Avey et al. On the other hand, the studies by Caza, Bagozi, Levy and Caza in New Zealand and by Rus, Baban, Jesus and Andrei in Romania offered evidence that supported the four-factor structure of the instrument, represented by one general second-order factor. In the latter study, however, an item had to be reallocated from the hope scale to the self-efficacy scale to obtain a good goodness of fit index.

In the study Viseu et al. Likewise, in a recent study on the invariance of the PCQ, Wernsing found, in samples of workers from the same organization in 12 countries, that psycap was best described by a three-factor structure, in which the optimism items were eliminated. Based on these considerations, the objective of this study was to present evidence of internal structure validity, internal consistency, convergent validity and invariance by gender, type of sample and age range for the Psychological Capital Questionnaire - Short Version PCQ in Brazilian samples.

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In total, subjects participated, being women These participants came from three independent studies. The first sample consisted of subjects In this group, The second sample consisted of individuals In this sample, The third sample consisted of individuals What the job characteristics are concerned, It should be highlighted that all ethical procedures for research involving human beings were guaranteed.


The PCQ consists of 12 items, answered on a six-point Likert scale ranging from 1 I strongly disagree to 6 I strongly agree. The original structure of the scale proposed four factors, which are: The instrument consists of four items, answered in different types of seven-point scales.

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The instrument consists of 10 items, being six positive and four negative, and assesses the perceived stress construct through a one-factor dimension. The items are answered on a Likert frequency scale ranging from never 0 to always 4. The questionnaire is answered on a Likert scale ranging from never 0 to almost every day 3 , respectively. This estimation method is useful for variables with non-normal distribution, and was used as the sample did not present multivariate normality for all items.

Three concurrent models were tested: The goodness of fit indices used to assess the adequacy of the models were: Next, three multigroup confirmatory factor analyses MGCFA were executed to investigate the invariance of the measure for different groups, that is: The objective of the multigroup analyses was to investigate to what extent the PCQ could be considered an equivalent instrument for both independent samples, and also for men, women, young people, adults and elderly.

If the model was not supported, then the instrument structure cannot be considered equivalent for the different groups. This model investigates the equivalent importance of the items in the calculation of the factor score. The cut-off points to interpret the indices are the same as mentioned earlier.

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Rainbows in the mind. An adjusted boxplot for skewed distributions. Based on these considerations, the objective of this study was to present evidence of internal structure validity, internal consistency, convergent validity and invariance by gender, type of sample and age range for the Psychological Capital Questionnaire - Short Version PCQ in Brazilian samples. Austrian Journal of Statistics , 34, Validation and psychometric properties of the Brazilian version of the Subjective Happiness Scale. We use cookies to help provide and enhance our service and tailor content and ads.

Finally, to enhance the validity evidence of the PCQ, the convergent validity of the questionnaire was investigated using different correlated psychological constructs. Thus, the PCQ was correlated Spearman correlations with the constructs satisfaction with life, subjective happiness, perceived stress and depression samples 1 and 2. Moderate and positive correlations are expected between the PCQ general factor and subdimensions and satisfaction with life and subjective happiness, and moderate and negative correlations between the PCQ general factor and subdimensions and perceived stress and depression.

Using the total sample, three concurrent models were mutually compared. As demonstrated in Table 1 , the single-factor model does not present acceptable fit levels. The models with four correlated factors and the model of second-order Psychological Capital present adequate and virtually identical fit levels. Based on these results, we chose to work with the second-order model. Figure 1 presents the structure and factor loadings of the model adopted. Based on the chosen model, the invariance of the scale was tested for the three independent sample, as well as for gender men and women and for the different age groups young people, adults and elderly.

To assess the convergent validity of the PCQ, its general factor and subscales, they were correlated with the scores of other psychological constructs: The results are displayed in Table 3. As shown, the general scale and the subscales of the PCQ presented moderate positive correlations with satisfaction with life, subjective happiness, as well as moderate negative correlations with depression and perceived stress.

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Based on earlier studies e. The confirmatory factor analysis presented inadequate fit levels for the single-factor structure, while the four-factor and second-order models were found plausible, with similar fit levels. Therefore, we chose to apply the second-order model in the study because, as mentioned, it permits calculating the factor scores for the general dimension psychological capital and for the specific dimensions hope, self-efficacy, resilience and optimism.

It is important to highlight, however, that the factor score of the general dimension Psychological Capital can only be calculated after modeling the other four specific dimensions.

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Possible explanations for the fact that this item obtained a loading below the others can be raised. To test the invariance of the PCQ, we tested to what extent the factor structure configural invariance and factor loading metric invariance and the item intercepts scalar invariance were similar for different samples.

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The results suggested that the PCQ was compatible among samples 1, 2 and 3, and also for men and women and young people, adults and elderly. These results are important for the PCQ, as they demonstrate that the instrument can be used in a wide range of samples and that these samples can be mutually compared in an unbiased manner Sass, Therefore, positive psychological capital is associated with higher rates of wellbeing and lower psychopathology levels. The Psychological Capital Questionnaire PCQ presented satisfactory psychometric properties, demonstrating different evidences of validity in the Brazilian context.

In addition, it was demonstrated that the scale can be applied to young, adult and elderly men and women and workers with different job affiliations. Finally, it should be highlighted that this study comes with some limitations. The exclusive use of a convenience sample does not permit the extrapolation of the data to other contexts. OneSided Hypotheses in a Multinomial Model.

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Statistics for Industry and Technology coverage of important topics relating to the theory, methods, and applications of goodness-of-fit tests and model validity. Goodness-of-Fit Tests and Model Validity (Statistics for Industry and Technology) (): C. Huber-Carol, N. Balakrishnan, M. Nikulin, .

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