Idea Transcript
Hierarchical regression This example of hierarchical regression is from an Honours thesis – hence all the detail of assumptions being met. In an undergraduate research report, it is probably acceptable to make the simple statement that all assumptions were met.
3.2.2 Predicting Satisfaction from Avoidance, Anxiety, Commitment and Conflict Prior to conducing a hierarchical multiple regression, the relevant assumptions of this statistical analysis were tested. Firstly, a sample size of 96 was deemed adequate given five independent variables to be included in the analysis (Tabachnick & Fidell, 2001). The assumption of singularity was also met as the independent variables (Avoidance, Anxiety, Commitment and Conflict) were not a combination of other independent variables. An examination of correlations (see Table 2) revealed that no independent variables were highly correlated, with the exception of Conflict and Satisfaction. However, as the collinearity statistics (i.e., Tolerance and VIF) were all within accepted limits, the assumption of multicollinearity was deemed to have been met (Coakes, 2005; Hair et al., 1998). Extreme univariate outliers identified in initial data screening were modified as above. An examination of the Mahalanobis distance scores indicated no multivariate outliers. Residual and scatter plots indicated the assumptions of normality, linearity and homoscedasticity were all satisified (Hair et al., 1998; Pallant, 2001). A four stage hierarchical multiple regression was conducted with Satisfaction as the dependent variable. Social Desirability was entered at stage one of the regression to control for socially desirable responding. The Attachment variables (Avoidance and Anxiety) were entered at stage two, Commitment at stage three and Conflict at stage four. The Relationship variables were entered in this order as it seemed chronologically plausible given attachment is relevant from infancy, whereas commitment and conflict issues occur once a person is in a relationship. Intercorrelations between the multiple regression variables were reported in Table 2 and the regression statistics are in Table 3.
Table 3 Summary of Hierarchical Regression Analysis for Variables predicting Satisfaction Variable Step 1 Social Desirability
t
β
.21
2.01*
sr2
.02
.24
.00
Avoidance
-.56
-5.86***
.16
Anxiety
-.26
-2.68**
.03
Step 3 Social Desirability
.01
∆R2
.21
.04
.04
.77
.60
.55
.81
.66
.06
.87
.77
.11
.04
Step 2 Social Desirability
R2
R
.20
.00
Avoidance
-.38
-3.82***
.06
Anxiety
-.26
-2.97**
.03
Commitment
.31
3.97***
.06
Step 4 Social Desirability
-.02
-.36
.00
Avoidance
-.20
-2.25*
.01
Anxiety
-.08
-1.02
.00
Commitment
.26
4.02***
.04
Conflict
-.50
-6.26***
.11
Note. N = 94; *p < .05, **p < .01, ***p< .001
The hierarchical multiple regression revealed that at Stage one, Social Desirability contributed significantly to the regression model, F (1,90) = 4.05, p< .05) and accounted for 4.3% of the variation in Satisfaction. Introducing the Attachment variables explained an additional 55.2% of variation in
Satisfaction and this change in R² was significant, F (2,88) = 60.10, p < .001. Adding Commitment to the regression model explained an additional 6.2% of the variation in Satisfaction and this change in R² was significant, F (1,87) = 15.74, p < .001. Finally, the addition of Conflict to the regression model explained an additional 10.7% of the variation in Satisfaction and this change in R² square was also significant, F (1,86) = 39.18, p < .001. When all five independent variables were included in stage four of the regression model, neither Social Desirability nor Anxiety were significant predictors of Satisfaction. The most important predictor of Satisfaction was Conflict which uniquely explained 11% of the variation in Satisfaction. Together the five independent variables accounted for 76.5% of the variance in Satisfaction.