In this chapter, I will describe the steps towards reaching a factor model that both fits with the data, and is theoretically grounded. A balance between a good model fit and explanation power of the model is required. The focal construct of Pro Diversity Leadership (PDL) will carefully be examined whether or not it consists of multiple sub-constructs: which model fits best with both theory and data. For empowering leadership and temporal leadership, the focus is on reestablishing what the original research on the respective constructs showed: that the constructs are valid in content, and that they are reliable, as indicated by Cronbach’s Alpha. After the factor models are established, the discriminant validity of PDL will be assessed: is it statistically different from the constructs of empowering leadership and temporal leadership?
After discussing the examination of the PDL construct, I will show the analysis on the proximal and distal effects of PDL, which are formulated in hypotheses 3 through 6.
Empowering leadership
In its original research, Empowering Leadership (EL) was measured using four multi-item subscales (Ahearne, Mathieu, & Rapp, 2005). In the Ahearne et al. (2005) study, the underlying dimension of
“empowering behaviors” was found, with a Cronbach’s alpha of 0.88, depicting a high internal consistency. Theoretically, this is justified: Ahearne et al. (2005) establish a theoretical framework in which the four subscales of comparable behavior styles are so closely related, that it is theoretically sound to summate the scale of EL. Therefore, an internal consistency test suffices to determine whether the seven EL items contribute to the factor of Empowering Leadership. The reliability coefficient, which is measured by Cronbach’s Alpha is computed in SPSS. An α of 0.82 was found, which is well above the generally considered lower limit of 0.70 (Hair & Black, 2009). Furthermore, α does not increase when deleting items, and the item-to-total correlations all exceed the 0.50 base mark (Hair & Black, 2009).
Temporal Leadership
For Temporal Leadership, it is difficult to make a theoretically grounded subdivision of factors based on the seven items in the questionnaire. Judging from the questions, it is hard to separate them in
categories, so up to this point I expect a one-factor model to fit the data, as found by Gevers et al.
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(2004). Just like for EL, it was previously established that TL conforms to conceptual definition, and a factor analysis in SPSS undoubtedly shows unidimensionality (see appendix A). The reliability coefficient, calculated with SPSS, gives α = 0.854, which is a good score compared to the cut-off value of 0.70 (Hair &
Black, 2009). Just as with EL, α does not increase upon deletion of items, and the item-to-total correlations exceed 0.50.
Pro-diversity leadership
Although Pro Diversity Leadership was previously coined by Rispens et al. (2012), it was not thoroughly established with data, which is one of the goals of my research. Therefore, I approach a factor model of PDL with an open-minded view, and carefully consider the options through confirmatory factor analysis.
Table 3: PDL questionnaire items
PDL01 Our team leader clarifies the value of the various functional areas that are present in this team to the team members
PDL02 Our team leader explains clearly why various functional areas are needed for new product development
PDL03 Our team leader tries to convince the team members of this new product development team that various functional areas are useful for the project
PDL04 Our team leader tries to make the members of this new product development team eager to use the different views
PDL05 Our team leader gives the team members tools to handle functional diversity in this team
PDL06 Our team leader encourages collaboration among team members from all the functional areas that are present in the team
Looking at the six items that tap into PDL related issues (see table 3), two subdivisions of items seem possible. Firstly, PDL01 and PDL02 together might form a factor called “Informing on pro-diversity benefits” and PDL03 through PDL06 could be “Encouraging pro-diversity habits”. Another possible division could be PDL01 through PDL03 which would be “Informing PDL” where PDL04 through PDL06 would be “Activating PDL”. Naturally, the third alternative is that all items form a single factor, namely PDL.
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Confirmatory Factor Analysis (CFA) is a multivariate tool that allows comparison between theory-based predicted covariance matrices and the actual covariance matrix computed from the raw data. The closer these two matrices are, the better the models will fit (Hair & Black, 2009). From theory, I defined three possible models. To judge which of these models best resembles reality (represented by the
questionnaire data), the models are run to see which has the best fit. Table 4 shows the output generated by Lisrel upon running the models.
Table 4: Model fit for PDL models (CFA)
Model # Variables Factors RMSEA CFI GFI χ2 df Δχ2 (Δdf)
1 PDL01-06 PDL 0.132 0.961 0.942 114.01* 9 -
2 PDL01,02
PDL03-06
PDL 1 PDL 2
0.121 0.971 0.955 87.02 * 8 26.99 (1)
3 PDL01-03
PDL04-06
PDL 1 PDL 2
0.080 0.987 0.979 42.48 * 8 71.53 (1)
*P<0.001
All three models are acceptable in terms of GFI and CFI: a lenient off value of >0.90 or a stricter cut-off of >0.95 (Hair & Black, 2009) is achieved by all models. Judging from RMSEA, model 3 has a good fit (generally <0.08 is acceptable). All measures show improvement when comparing models 2 and 3 to the baseline model 1, and the Δχ2 (Δdf) of 71.53 shows that the model is improved significantly (>3.84 (1df)).
Clearly, model 3 resembles the data best which means that from now on, PDL will be divided in Informing PDL and Activating PDL.
Through confirmatory factor analysis, I have established that PDL01 – PDL03 as Informative PDL, and PDL04 – PDL06 as Actionable PDL fit the data best. To test their internal consistencies, their Cronbach’s Alphas are computed using SPSS. Informative PDL has an α of 0.884, and Actionable PDL had an α of 0.793, both of which are above the cut-off value of 0.7, and below the redundancy cut-off of 0.95.
Hypothesis 1 stating that all PDL related items contribute to the measure of PDL such that they are
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specific enough while being non-redundant is partially supported: CFA indicated that a two-factor model is preferred over a single-factor model. However, both factors are internally consistent.
Discriminant Validity
To test for discriminant validity, I performed CFA. Firstly, the models combining the PDL measures and TL will be provided, after which the results will be discussed. Secondly, the possible PDL and EL models will be provided with a discussion of the results.
Pro-diversity Leadership and Temporal Leadership
To determine that both PDL measures are significantly different from each other and from TL, models containing al possible combinations need to be tested.
These models have been tested using the same fit indices as previously for the PDL models. The results from the Lisrel computations can be found in table 5.
Table 5: CFA output of PDL and TL models
Model # Variables Factors RMSEA CFI GFI χ2 df Δχ2 (Δdf)
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The baseline model of TL combined with both PDL measures (model 1) shows a bad fit in all fit indices.
Models 3 and 4, which combine either of the PDL measures with TL, also perform poorly. Model 5, where the three factors are separated scores best on all indices. Even though the RMSEA is slightly above the 0.08 cut-off, CFI and GFI are above 0.90 and therefore sufficient. Δχ2 (Δdf) shows dramatic improvement over the baseline model, as well as significant improvement over alternative models 3 and 4 (Δχ2 (Δdf) >
3.84 (1); > 5.99 (2); > 7.81 (3)). Separating the two PDL measures (model 5) proves again to give a better model fit than when they are combined (model 2).
Pro-diversity Leadership and Empowering Leadership
To determine that both PDL measures are significantly different from each other and from EL, models containing al possible combinations have been tested, just like previously with PDL and TL. The model definitions can be found in appendix A.
These models will be tested using the same fit indices as previously for the PDL and TL models. The results from the Lisrel computations can be found below in table 6.
Table 6: CFA output PDL and EL
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In none of the five models combining PDL and EL a good model fit was found1. However, the point of this CFA analysis is to prove that the PDL constructs and EL are significantly different from each other, and that point can be made without any of the models achieving good model fit. The best results are reported for model 5, with the factors of PDL 1, PDL 2 and EL separated. The improvement over the baseline model 1, and alternative models 2, 3 and 4 is significant. This proves that both constructs of PDL are statistically different from each other and from EL (Δχ2 (Δdf) > 3.84 (1); > 5.99 (2); > 7.81 (3)).
Hypothesis 2, stating that PDL is statistically distinct from temporal leadership and empowering leadership, is fully supported, providing the CFA analyses in this chapter.
Criterion Validity
In hypotheses 3 through 6, the proximal and distal effects of pro-diversity leadership are described. In the following section, I will show the analysis that has been executed to test these hypotheses. Table 7 shows the means, standard deviations and correlations of all involved measures.
Hierarchical regression was used to test the hypotheses. In step 1, the control variables were regressed against the dependent variable, and in step 2 the hypothesized independent variable was added. For interaction effects, step 3 was added, to see if the interaction better explained the model than only the direct effects.
1 Further analysis revealed that splitting EL up into sub constructs resulted in sufficient model fit. The researchers that invented EL constructed it using four subscales, which were coherent to such extent that they could be summated to a single scale (Ahearne, Mathieu, & Rapp, 2005). These subscales were clearly identified in my study, explaining why the model fit was not satisfactory. However, it is out of the scope of this research to optimize the internal consistency of a previously established construct. Therefore, I sufficed with the above mentioned confirmatory factor analysis, even though none of the models shows an adequate fit.
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Table 7: Means, standard deviations and correlations
Correlations
Mean
Std.
deviation N 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
1. General Team Performance 5,53 0,69 81 -
2. Task Conflict 2,57 0,58 81 -,241* -
3. Informing Pro-Diversity Leadership
4,69 0,84 81 ,548** -,078 -
4. Activating Pro-Diversity Leadership
4,75 0,82 81 ,658** -,030 ,777** -
5. Information Elaboration 3,8 0,49 81 ,682** -,171 ,510** ,537** -
6. Team Identification 3,6 0,58 81 ,343** ,035 ,234* ,406** ,463** -
7. Task Interdependence 4,49 0,45 81 -,046 ,358** ,034 ,014 -,042 -,084 -
8. Functional Diversity 0,5 0,25 81 -,274* ,237* ,030 -,134 -,204 -,108 ,159 -
9. Team Size 5,05 2,84 81 ,036 ,142 -,047 ,028 ,058 ,042 ,189 ,156 -
10. Project duration in months 24,4 34,1 77 ,181 -,032 ,108 ,169 ,244* ,147 ,056 -,281* -,063 -
*. Correlation is significant at the 0.05 level (2-tailed).
**. Correlation is significant at the 0.01 level (2-tailed).
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Hypothesis 3a: Positive interaction effect of PDL on Functional Diversity – Team Performance link Since we saw in hypotheses 1 and 2 that pro-diversity leadership was split in Informing pro-diversity leadership and Activating diversity leadership, I have analyzed both cases. For informing pro-diversity leadership, a significant interaction effect was found, indicating that high levels of informing pro-diversity leadership prevent to some extent general team performance to drop with high levels of functional diversity (β= 0.265, p < 0.05, figure 6 & table 8). Therefore, for informing pro-diversity leadership I confirm the hypothesis, noting that the relation between functional diversity and general team performance is negative instead of positive (see hypothesis 4). However, team identification still has a positive influence on this relationship.
Figure 6: Interaction effect of informing pro-diversity leadership on functional diversity - general team performance link
For activating pro-diversity leadership, no significant interaction effect was found (table 9), which means that for activating pro-diversity leadership the hypothesis is not confirmed.
2 3 4 5 6
Low F. Diversity High F. Diversity
General Team Performance
Low Inf. PDL High Inf.
PDL
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Table 8: Regression coefficients of informing pro-diversity leadership’s interaction on Functional Diversity – GTP link
General Team
Performance
Step 1: Task interdependence 0,000
Control Variables Team size 0,068
Project duration 0,186
R² 0,038
Step 2: Task interdependence 0,009
Direct effect Team size 0,132
Project duration 0,047
Functional diversity -0,292**
Informing pro-diversity leadership 0,551**
R² 0,387
ΔR² 0,349**
Step 3: Task interdependence -0,024
Interaction effect Team size 0,148
Project duration 0,045
Functional diversity -0,292**
Informing pro-diversity leadership 0,570**
Functional Diversity * Informing PDL 0,265**
R² 0,455
ΔR² 0,069**
Note: N=81; Standardized coefficients are reported; ** = p<.01, * = p<.05, † = p<.10
Table 9: Regression coefficients of activating pro-diversity leadership’s interaction on Functional Diversity – GTP link
General Team
Performance
Step 1: Task interdependence 0,000
Control Variables Team size 0,068
Project duration 0,186
R² 0,038
Step 2: Task interdependence -0,005
Direct effect Team size 0,069
Project duration 0,031
Functional diversity -0,187†
Activating pro-diversity leadership 0,602**
R² 0,438
ΔR² 0,400**
Step 3: Task interdependence -0,001
Interaction effect Team size 0,075
Project duration 0,049
Functional diversity -0,228*
Activating pro-diversity leadership 0,582**
Functional Diversity * Activating PDL 0,140
R² 0,455
ΔR² 0,017
Note: N=81; Standardized coefficients are reported; ** = p<.01, * = p<.05, † = p<.10
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Hypothesis 3b: PDL has a negative relationship with Task Conflict
The hypothesized negative relation between pro-diversity leadership and task conflict was not confirmed: neither informing pro-diversity leadership nor activating pro-diversity leadership shows a significant relation with task conflict (tables 10 and 11).
Table 10: Regression coefficients of informing pro-diversity leadership
Task Information Team
Conflict Elaboration Identification
Step 1: Task interdependence 0,293* 0,042 -0,051
Control Variables Team size 0,095 0,087 0,084
Project duration -0,042 0,247* 0,155
R² 0,107 0,070 0,030
Step 2: Task interdependence 0,297* 0,000 -0,07
Direct effect Team size 0,093 0,117 0,098
Project duration -0,038 0,198 0,133
Informing
pro-diversity leadership -0,037 0,490** 0,228*
R² 0,108 0,305 0,081
ΔR² 0,001 0,235** 0,051*
Note: N=81; Standardized coefficients are reported; ** = p<.01, * = p<.05, † = p<.10
Table 11: Regression coefficients of activating pro-diversity leadership
Task Information Team
Conflict Elaboration Identification
Step 1: Task interdependence 0,293* 0,042 -0,051
Control Variables Team size 0,095 0,087 0,084
Project duration -0,042 0,247* 0,155
R² 0,107 0,070 0,030
Step 2: Task interdependence 0,291* 0,009 -0,078
Direct effect Team size 0,094 0,072 0,072
Project duration -0,048 0,166 0,089
Activating
pro-diversity leadership 0,038 0,484** 0,395**
R² 0,108 0,296 0,180
ΔR² 0,001 0,226** 0,151**
Note: N=81; Standardized coefficients are reported; ** = p<.01, * = p<.05, † = p<.10
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Hypothesis 3c: PDL has a positive relationship with Information Elaboration
Informing pro-diversity leadership indeed showed a strong positive relation with information elaboration, as hypothesized (β= 0.490, p < 0.01; table 10). It shows that next to informing pro-diversity leadership, also the control variable of Project Duration, or how long the project has been running to date, shows a positive relation with information elaboration. The R squared change between the first (control variables) and second model (control variables and informing pro-diversity leadership) is significant (p<0.01), showing a better model fit, hence confirming that informing pro-diversity leadership influences information elaboration above and beyond the control variables.
Just like informing pro-diversity leadership, activating pro-diversity leadership showed a strong positive relation with information elaboration (β= 0.484, p < 0.01; table 11). In this regression, project duration was not significantly related to information elaboration anymore. Altogether, these results confirm hypothesis 3c.
Hypothesis 3d: PDL has a positive relationship with Team Identification
Informing pro-diversity leadership showed a positive relationship with team identification as hypothesized (β= 0.228, p < 0.05; table 10). Activating pro-diversity leadership also shows a positive relationship with team identification, which is remarkably stronger (β= 0.395, p < 0.01; table 11).
Therefore, hypothesis 3d was confirmed.
Hypothesis 4: Functional Diversity has a positive relationship with Team Performance As shown in table 10, a significant negative relation (β= -0.249, p < 0.05) was found between
functional diversity and general team performance. Hypothesis 4, stating a positive relation between the two, is therefore not confirmed.
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Table 12: Regression coefficients of functional diversity
Task Information General Team
Conflict Elaboration Performance
Step 1: Task interdependence 0,293* 0,042 0,000
Control Variables Team size 0,095 0,087 0,068
Project duration -0,042 0,247* 0,186
R² 0,107 0,07 0,038
Step 2: Task interdependence 0,252** 0,081 0,047
Direct effect Team size 0,073 0,108 0,094
Project duration 0,021 0,189 0,115
Functional Diversity 0,220† -0,204† -0,249*
R² 0,149 0,106 0,091
ΔR² 0,042† 0,036* 0,054*
Note: N=81; Standardized coefficients are reported; ** = p<.01, * = p<.05, † = p<.10
Hypothesis 5a: Functional Diversity is positively related with Team Performance, mediated by Task Conflict
The positive relation between functional diversity and task conflict hypothesized in hypothesis 5a is confirmed (table 12; β= 0.220, p < 0.10). The positive relation between task conflict and general team performance could however not be confirmed. Instead, a negative relation was found (β= -0.264, p <
0.05; table 13). Initially, it was found that task conflict fully mediates the relation between functional diversity and general team performance, however this conclusion was to be carefully considered, since the significance of the mediator is only below the most lenient cut-off of p<0.10 (p=0.068) whereas the predictor only slightly surpasses this cut-off (p=0.104). Therefore, Sobel’s test is
executed to determine whether or not we have a case of full mediation. As Sobel’s test gives p>0.10 (p=0.15), I determined that full mediation is not the case. Task conflict partially acts as a mediator between functional diversity and general team performance, however the mediated relationship is negative instead of positive.
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Table 13: Regression coefficients of task conflict on general team performance
General Team
Performance
Step 1: Task interdependence 0
Control Variables Team size 0,068
Project duration 0,186
R² 0,038
Step 2: Task interdependence 0,078
Direct effect Team size 0,094
Project duration 0,174
Task conflict -0,264*
R² 0,100
ΔR² 0,062†
Note: N=81; Standardized coefficients are reported; ** = p<.01, * = p<.05, † = p<.10
Functional Diversity
Team Performance
Pro-diversity Leadership Task Conflict
N.S.
0.220 -0.264*
-0.249*
Note: Standardized coefficients are reported; ** = p<.01, * = p<.05, = p<.10
Figure 7: Overview of task conflict related path coefficients
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Hypothesis 5b: Functional Diversity is positively related with Team Performance, mediated by Information Elaboration
As shown before, functional diversity and general team performance are negatively related.
Furthermore, it shows that functional diversity and information elaboration were negatively related (β= -0.204, p < 0.10; table 12). On the other hand, a very strong relationship was found between information elaboration and general team performance (β= 0.666, p < 0.01; table 14). Full mediation was found: the causal variable functional diversity was found to be non-significant whereas the mediator information elaboration still showed a strong relation (β= 0.644, p < 0.01) when both the causal variable and the mediator were regressed together. Therefore, hypothesis 5b is confirmed partially: full mediation does take place, however the mediated relation is negative instead of positive.
Table 14: Regression coefficients of information elaboration on general team performance
General Team
Performance
Step 1: Task interdependence 0,000
Control Variables Team size 0,068
Project duration 0,186
R² 0,038
Step 2: Task interdependence -0,028
Direct effect Team size 0,011
Project duration 0,021
Information elaboration 0,666**
R² 0,450
ΔR² 0,413**
Note: N=81; Standardized coefficients are reported; ** = p<.01, * = p<.05, † = p<.10
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Note: Standardized coefficients are reported; ** = p<.01, * = p<.05, = p<.10 0.490** / 0.484**
Informing / Activating
Figure 8: Overview of information elaboration related path coefficients
Hypothesis 6: Positive interaction effect of Team Identification on the Functional Diversity – Team Performance link
As identified earlier, functional diversity and general team performance were negatively related.
However, Team Identification positively influenced this negative relation such that when team identification is high, the negative effect of diversity on general team performance is significantly less than when team identification is low (β= 0.236, p < 0.05, figure 9 & table 15). Therefore, results confirm a moderation effect of team identification on the functional diversity – general team performance link.
Figure 9: Interaction effect of team identification on functional diversity - general team performance link
2 3 4 5 6
Low F. Diversity High F. Diversity
General Team Performance
Low Team ID High Team ID
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Table 15: Regression of interaction effect of team identification on functional diversity - general performance
General Team
Performance
Step 1: Task interdependence 0,000
Control Variables Team size 0,068
Project duration 0,186
R² 0,038
Step 2: Task interdependence 0,057
Direct effect Team size 0,071
Project duration 0,081
Functional diversity -0,230†
Team identification 0,249*
R² 0,151
ΔR² 0,114*
Step 3: Task interdependence 0,082
Interaction effect Team size 0,059
Project duration 0,099
Functional diversity -0,264*
Team identification 0,199†
Functional Diversity * Team identification 0,236*
R² 0,202
ΔR² 0,051*
Note: N=81; Standardized coefficients are reported; ** = p<.01, * = p<.05, † = p<.10
Functional
Note: Standardized coefficients are reported; ** = p<.01, * = p<.05, = p<.10 Informing
Figure 10: Moderation model with informing PDL
Functional
Note: Standardized coefficients are reported; ** = p<.01, * = p<.05, = p<.10 Activating
Figure 11: Moderation model with activating PDL
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