Rasch Analysis of the Proactive Personality Scale

Introduction

Developed to assess a person’s proactive disposition, the Proactive Personality Scale (PPS) is widely used in industrial and organisational psychology research (see Gerhardt, 2009; Li et al., 2010). The PPS was developed by Bateman and Crant (1993) and Seibert et al. (1999) in response to the growing recognition that understanding the antecedents of proactive behaviour in various work domains would require a self-report measure that could assess an individual’s proactive tendency. Proactive personality is defined as a dispositional tendency that is relatively unconstrained by situational forces and is held to be relatively stable over time (Crant & Bateman, 2000; Parker & Bindl, 2016; Seibert et al., 2001). Recent meta analytic work demonstrated that more than 50% of variance in proactive personality is unrelated to the Big Five personality traits (also known as the five-factor model; Gerber et al., 2011; Gosling et al., 2003; McCrae & Costa, 2008, 2013), suggesting its uniqueness (Spitzmuller et al., 2015). Considered a trait, proactive personality is enduring and relatively stable (Seibert et al., 1999). Previous research has evaluated the psychometric properties of the 6-item PPS using classical test theory (CCT; Claes et al., 2005). Despite the promising results reported for the scale using the traditional CTT, there is a need to provide further validity evidence for the 6-item PPS using modern test theory. This accumulated evidence would clarify the factor structure of the construct and provide further support to the use of the scale’s test scores. Moreover, to date, there is no validity information on the 6-item PPS from Ghana. Gathering validity evidence for the PPS in Ghana would extend the scale to a new cultural context, as it would help to draw inferences about the proactive personality dispositions of individuals in Ghana.

Various researchers, working independently, have used various versions of the PPS, including 10-item, 6-item, 5-item, and 4-item, to assess proactive personality (see Chan, 2006; Ji et al., 2019; Liao, 2015; Pan et al., 2018; Parker, 1998; Parker & Sprigg, 1999; Parker et al., 2006; Wang et al., 2017). Claes et al. (2005) investigated the factor structure of the 10-item, 6-item, 5-item, and 4-item versions of the PPS using cross-cultural data from Finland, Belgium, and from Spain. Results from confirmatory factor analysis (CFA) concluded that, the 6-item version (hereafter called PPS-6) demonstrated the most optimal factor solution that was internally consistent across the three samples (Finland, α = .78; Belgium, α = .79; and Spain, α = .86). See also Hu et al. (2018), Li et al., (2010), and Vermooten et al. (2019).

The CTT, although useful, cannot make the PPS-6 immune from psychometric criticism because it has inherent limitations. For example, the CTT cannot establish the response category functioning of the PPS (see Kean et al., 2017; Petrillo et al., 2015). Raykov and Marcoulides (2011) highlighted other limitations of CTT:

An important limitation of CTT is that it does not place routinely in the center of its concerns how individuals at different levels of the construct studied (ability, trait, attribute) perform on the components, or items, of an instrument aimed at measuring that underlying latent dimension. (p. 247)

The Rasch rating scale model

The Danish mathematician Georg Rasch (1960) introduced a logistic measurement model for tests that consist of dichotomous items. The simple logistic model states that the probability that person n would correctly answer item i, P n i , is a function of the ability of the person, B n and the difficulty of the item, D i . The model is mathematically expressed as

P n i = e ( B n − D i ) 1 + e ( B n − D i )

(1)

P nik = e ( B n − ( D i + F j ) ) 1 + e ( B n − ( D i + F j ) )

(2)

The rating scale model is used to estimate for each item a single location parameter, D i , and m – 1 thresholds parameters. F j represents the location on the trait continuum, where, relative to D i , a person has a 50% chance of endorsing category j, rather than the category preceding it. One set of threshold parameters is estimated for the complete set of items. The difficulty of threshold j of item i is found by adding F j to D i . In this sense D i serves to shift the set of m – 1 category thresholds up or down the latent trait continuum, depending on the overall difficulty of the item (Bond & Fox, 2015; Embretson & Reise, 2000; Wright & Masters, 1982).

The rating scale model, like the simple logistic model, is built on the principle of specific objectivity (Andrich & Marais, 2019; Rasch, 1960). This principle holds that the comparisons of persons should be independent of particular instruments/measures. Similarly, comparisons of items should be independent of particular individuals. Rasch models may be seen as a prescription for objective measurement (Bond & Fox, 2015), which requires that the set of items should be unidimensional, pairs of items should be locally independent, the slopes of the empirical item characteristic curves should be equivalent, and the difficulty or location of items should be invariant across different classes of persons (Bond & Fox, 2015; Wright & Masters, 1982).

In the context of Rasch measurement the requirement of unidimensionality is commonly assessed by subjecting the standardised residuals of an analysis to a principal components analysis. In this respect, it is expected that there will be no structure in the residuals. Local independence is assessed by examining the correlations of pairs of standardized residuals, where it is expected that the residual correlation pairs will be close to zero. The uniformity of the slopes of the item characteristic curves (i.e. empirical item discrimination) is commonly assessed with reference to infit and outfit item fit mean square statistics, which have an expected value of 1.00 if the data fit the model. Values >1.00 indicate underfit (i.e. flatter slopes than expected), whereas values <1.00 indicate overfit (i.e. steeper slopes than expected). Infit and outfit mean squares between 0.75 and 1.30 may be considered acceptable. The mean squares can also be transformed to approximate t-values, which may be used to test the null hypothesis of perfect fit. The invariance of item locations across different classes of persons is assessed by comparing the item locations across the different classes.

An additional feature of the rating scale model is that it allows for an evaluation of the functioning of the ordered response categories. In this regard, it is expected that the category thresholds will be ordered in value in the same order as the response categories (Adams et al., 2012). Disordered thresholds may indicate that some response categories are under endorsed, which may be a problem when it is expected that the category would be endorsed more frequently. In the absence of such expectations disordered thresholds do not necessarily indicate misfit [but see Andrich (2004, 2013) for a contrary point of view]. Finally, it should be noted that Rasch models represent an ideal and that empirical data will always fail to fit the model to some degree. In this respect, the focal issue is whether the misfit is small enough to allow for useful measurement to take place rather than if the data fit the model perfectly.

Proactive personality and gender

In their meta-analytic review, Spitzmuller et al. (2015) examined gender differences in proactive personality across the 17-, 10-, and 6-item versions of the PPS. Using d statistics, they found no gender differences in proactive personality both in student and working adult samples. However, they observed small gender differences in proactive personality relative to the version of the measure used. They noted that the 17-item version was the most robust to contextual factors. This result suggests the need for a gender-invariance analysis on the PPS-6. As far as we know, no gender invariance analyses have been published on the PPS-6. Establishing that the items on the PPS-6 function invariantly across gender, would offer opportunities to meaningfully compare scores of individuals across gender groups in future research (see Davidov et al., 2014; Jones, 2019; Putnick & Bornstein, 2016).

Method

Results

Table 1 summarises the descriptive statistics of the items on the PPS-6.

OPEN IN VIEWER

Table 1.

Items and descriptive statistics of the PPS-6.

Item #	Item description	M	SD	Mode	Skew	Kurtosis	SE
1.	If I see something I don’t like, I fix it.	3.34	0.99	4	−0.38	−0.41	0.23
2.	No matter what the odds, if I believe in something I will make it happen.	3.53	1.02	4	−0.49	−0.22	0.23
3.	I love being a champion for my ideas, even against others' opposition.	3.47	0.98	4	−0.32	−0.36	0.23
4.	I excel at identifying opportunities.	3.42	0.99	4	−0.23	−0.46	0.23
5.	I am always looking for better ways to doing things.	3.58	1.00	4	−0.50	−0.17	0.23
6.	If I believe in an idea, no obstacle will prevent me from making it happen.	3.43	1.02	4	−0.36	−0.48	0.23

Note. PPS = Proactive Personality Scale.

Rasch analysis

We used the rating scale model to estimate person locations and item and threshold locations. These parameters were used to calculate expected scores of each person to each of the items. An unrotated principal components analysis of the standardised differences of observed and expected responses of the persons showed that the Rasch dimension explained 52.7% of the variance in the PPS-6. The eigenvalue of the first component was 1.3, which is less than the strength of two items. This indicated that the six items could be treated as if they measured a unidimensional construct. ¹ Further, the item residual correlations ranged from −.13. to −.34, which evidenced that the items could be treated as locally independent.

Table 2 summarises the functioning of the 5-point ordered category response scale. Each category attracted a fair number of responses, but it is noticeable that the “strongly disagree” category was unpopular relative to the other categories. The order of the Rasch-Andrich thresholds corresponded with the order of the response categories. In addition, average person measures advanced monotonically with each successive response category, and infit and outfit mean squares of the categories ranged from .90 to 1.22. Jointly, these results show that persons used the 5-point response scale as expected.

OPEN IN VIEWER

Table 2.

Summary statistics of the response category functioning.

Category	Frequency of responses	Percentage of responses	Average person measure	Infit mean square	Outfit mean square	Rasch-Andrich threshold
SD	76	3	−1.79	1.12	1.09
D	356	14	−0.82	0.91	0.90	−2.83
ND/A	760	31	0.22	0.96	0.98	−1.01
A	984	40	1.38	0.91	0.90	0.48
SA	288	12	2.92	1.22	1.10	3.36

Note. SD = strongly disagree, D = disagree, ND/A = neither disagree nor agree, A = agree, SA = strongly agree.

Examination of infit and outfit mean squares of the items indicated that five items had satisfactory fit, but that item 1 evidenced underfit, with infit mean square = 1.45 and outfit mean square = 1.65. Comparison of observed person responses with model expected responses to item 1 revealed that a small number of persons (n = 16, 3.7% of the total number of participants) largely contributed to the misfit of item 1. Setting these persons aside yielded satisfactory infit and outfit mean squares for all the items, but item 1 remained the worst fitting item (see Table 3). Infit mean square values ranged from 0.88 to 1.18 and outfit mean square values ranged from 0.87 to 1.23. In addition, the item-measure correlations ² indicated that each item related strongly to the trait that is measured by the PPS-6. Note, however, that the item-measure correlation of item 1 was clearly weaker than that of the remaining items. Figure 1 presents the empirical item characteristic curves, which link the latent trait to the expected item scores. Visual inspection shows that the slopes of the curves were essentially parallel, but that in the upper range of the trait, the curve of item 1 had a somewhat flatter slope than the remaining items.

OPEN IN VIEWER

Table 3.

Items, locations, item-measure correlations, and item fit statistics of the PPS-6 (N = 413).

Item	Item description	Item location	Standard error	Infit	Oufit	Item-measure correlation
4.	I excel at identifying opportunities.	.15	.07	1.00	1.01	.71
1.	If I see something I don’t like, I fix it.	.13	.07	1.18	1.23	.62
6.	If I believe in an idea, no obstacle will prevent me from making it happen.	.12	.07	0.93	0.89	.75
3.	I love being a champion for my ideas, even against others' opposition.	−.04	.07	0.88	0.87	.74
2.	No matter what the odds, if I believe in something I will make it happen.	−.11	.07	0.93	0.89	.75
5.	I am always looking for better ways to doing things.	−.24	.07	1.04	0.98	.72

Note. PPS = Proactive Personality Scale. Item locations are presented in descending order of item difficulty. Infit and outfit statistics are expressed as mean squares.

OPEN IN VIEWER

Figure 1.

Empirical Item Characteristic Curves of the PPS-6. The transparent circle highlights the misfit of item 1 in the upper range of the latent trait.

Differential item functioning

Table 4 summarises the results of the DIF analyses. Comparison of the item locations of the men and women by means of independent groups t-tests yielded no statistically significant differences (Bonferonni corrected α = .05/6 = .008). Note, however, that if treated individually, item 6 would be seen as demonstrating uniform DIF, with women finding the item more difficult to agree with. These results were mirrored by Mantel (1963) chi-square tests. Overall, the differences of the item locations of the men and women were small (the largest contrast was -.35 logits for item 6). These results indicate that men and women attached similar meaning to the items. An independent groups t-test of the person measures of the men (M = .70 logits, SD = 1.71) and the women (M = .89 logits, SD = 1.49 logits) indicated that the means of the two groups on the proactive trait did not differ statistically significantly, t(407) = −1.20, p = .232).

OPEN IN VIEWER

Table 4.

Differential item functioning across gender of the PPS-6.

	Item difficulties		DIF contrast	Joint S.E.	t	p	Mantel χ2	p
Item#	Men	Women
1.	.16	.09	.08	.15	.53	.60	.06	.79
2.	−.17	−.05	−.12	.15	−.82	.41	1.01	.31
3.	.01	−.10	.10	.15	.68	.49	.58	.44
4	.26	.03	.23	.15	1.60	.11	3.39	.07
5.	−.21	−.28	.06	.15	.42	.67	.61	.43
6.	−.05	.30	−.35	.15	−2.40	.02	7.48	.02

Note. PPS = Proactive Personality Scale.

Figure 2 is a Wright map that summarises the distributions of the men and women and the Andrich thresholds on the latent trait continuum. The distributions of the men and women were similar and roughly approximated normal distributions. The Wright map also shows the proper ordering of the Andrich thresholds, which covered a relatively large range of the latent trait continuum (ranging from about −3 logits to about 4 logits).

OPEN IN VIEWER

Figure 2.

Wright map of person distributions and locations of the andrich thresholds of the PPS-6. The Wright map plots the locations of the men and the women (as density distributions) and the Andrich thresholds of the items on the latent trait continuum. This Wright map shows that the person measures were widely distributed along the latent trait continuum. The trait distributions of both groups roughly approximated a normal distribution. The distributions of the men and women were similar. An Independent groups Welch t-test showed that the means of the men (M = .70 logits, SD = 1.71, SE = .12) and the women (M = .89 logits, SD = 1.48, SE = .10) were equivalent, t(407) = −1.20, p = .232.

Discussion

The aim of this study was to evaluate the psychometric properties of the 6-item Proactive Personality Scale (i.e. PPS-6) for recent Ghanaian university graduates using the Rasch rating scale model. We employed the model as a diagnostic tool with the aim of identifying measurement disturbances that could threaten the validity of person measures obtained with the PPS-6. In particular, we focused on whether (a) the PPS-6 measures a unidimensional trait, (b) the items were locally independent, (c) the 5-point ordered response categories functioned as intended, (d) the slopes of the item characteristic curves were parallel, and (e) the items had invariant locations for men and women. Taken together, the results showed that the data provided a good fit to the rating scale model and that there were no serious measurement disturbances in the data. In the paragraphs that follow, we discuss each of our results with reference to each of the potential measurement threats.

Our analysis of the standardised Rasch residuals demonstrated that the Rasch dimension dominated the data and that no additional meaningful dimensions could be extracted. This result is consistent with previous confirmatory factor analytic studies that provided support for the unidimensionality of the PPS-6 in Finland, Belgium and in Spain (Claes et al., 2005). See also Hu et al. (2018), Li et al. (2010), Parker (1998), and Vermooten et al. (2019). Inspection of the pairwise correlations of the standardized Rasch residuals revealed no salient violations of the principle of local independence. These results indicate that it is safe to combine the items into a total measure among Ghanaian university graduates.

The rating scale analysis also provided evidence for the suitability of the 5-point response rating scale employed by the PPS-6. Participants used the response categories as expected, such that persons with higher trait levels endorsed higher response categories. The Andrich thresholds were properly ordered, which indicated that each successive category becomes the modal category along the latent trait continuum.

Infit and outfit statistics of the items demonstrated that the items fit the rating scale model satisfactorily which means that the differences between persons’ observed responses and model expected responses were similar. These statistics, in conjunction with visual inspection of the empirical characteristic curves indicate that for the most part, the slopes of the curves were essentially parallel. A noticeable exception was observed for item 1, where even after removing persons who responded most unexpectedly, the empirical slope flattened more than expected in the upper range of the trait (see Figure 1). This indicates that persons with high trait levels scored somewhat lower than expected. We speculate that this disturbance can be attributed to the content of item 1 (“If I see something I don’t like, I fix it”) with some persons perhaps attaching a literal interpretation to the item. It is conceivable that persons with such an interpretation would respond in lower categories if they dislike physically fixing things, even if they have high levels of proactiveness.

Comparison of the locations of the item characteristic curves of men and women evidenced that none of the six items displayed DIF that would lead to a noticeable measurement disturbance. It appears safe to compare the scores of men and women. Our analysis also demonstrated that the mean person measures of the two groups were equivalent (within error). This result accords with those of Spitzmuller et al. (2015) who found proactive personality to be invariant across gender. Finally, a Wright map of the person distributions and Andrich thresholds demonstrated that the PPS-6 was appropriately targeted at the trait levels of recently graduated Ghanaians. As is commonly the case with the measurement of normal personality attributes, however, persons at the extreme ends of the trait distribution are not targeted very well.

The Rasch person reliability of the PPS-6 person measures was .80, which corresponded with the Cronbach’s coefficient alpha (.82) and McDonald’s coefficient omega (.82). These coefficients suggest that the scale yields measures with satisfactory reliability for research purposes in Ghana. The Cronbach alpha corresponds well with reliabilities reported by Claes et al. (2005) in Finland, Belgium, and in Spain.

Conclusions

Rasch analysis demonstrated that the PPS-6 is a highly promising measure of pro-activeness in the Ghanaian context among recent university graduates. The analysis allowed for fine-grained evaluations of the scale and its items. The few measurement disturbances that we detected were mild and we believe that the PPS-6 can safely be used with adult working men and women. Our results also extend the theoretical reach of the proactive personality concept to the Ghanaian context and potentially pave the way for further research into the precursors and consequences of the trait.