The 184 male patients in the dataset were aged 40–86 (M
= 68.46, SD
= 8.61) with advanced prostate cancer diagnoses, receiving treatment on CALGB 9840 [34
]. Patient characteristics are displayed in . The sample consisted largely of Caucasian (76.6%) and African-American (16.9%) patients, with a smaller proportion identifying themselves as Hispanic (4.9%) or “other” (1.6%).
Characteristics of Patients (N = 184)
displays the means, standard deviations, and Pearson correlation coefficients among the eleven items of the BPI. The present dataset satisfied all CFA requirements for normality, multicollinearity, residual values, and multivariate outliers.
Correlation Coefficients, Means, and Standard Deviations for Outcome Measures
During initial model specification, modification indices were examined to determine whether any of the residual variances had strong inter-correlations. Modification indices represent the expected chi-square change if a parameter if the model is freed [42
]. Consequently, adding correlations between residuals improves model fit. Strong correlations between the residual variances were observed as follows: “pain at its worst in the last 24 hours” and “describe your pain on average”; “pain at its least in the last 24 hours” and “describe your pain on average”; “pain at its least in the last 24 hours” and “how much pain do you have right now”; “describe your pain on average” and “how much pain do you have right now”; “interference with general activity” and “interference with mood”; “interference with mood” and “interference with relations with other people”; “interference with walking ability” and “interference with work”; and “interference with walking ability” and “interference with sleep.” For the subsequent analyses, these correlations were added to increase the overall fit for each model.
According to the fit indices (), Model 2 was a significant improvement over Model 1. Model 2 had a lower RMSEA value (0.096), a higher CFI value (0.950), and a significant change in chi-square given the corresponding change in degrees of freedom when compared to Model 1 (χ2(1) = 17.75, p < .05). Model 3 was statistically superior to Model 2 in terms of RMSEA (0.075), CFI (0.971), and change in chi-square given the corresponding change in degrees of freedom values (χ2(2) = 13.33, p < .05). From these results, Model 3 was selected as the best fit for the data (), with Model 2 treated as a suitable alternative representation in this sample. Standardized factor loadings for all models are displayed in .
Fit Indices for Confirmatory Factor Models in Overall Sample
Confirmatory Factor Model for the Three-Factor Solution
Standardized Factor Loadings and Factor Correlations by Model and Latent Construct (N = 184)
For each of the four multi-group analyses, a model was fit that simultaneously imposed constraints on all of the factor loadings and covariances. Placing these constraints forced the values to be equal across groups. This model was then compared to a baseline model where none of the factor loadings were constrained. is a display of the fit indices for the multi-group analyses. Since for each of the analyses there were no significant differences between the models in chi-square value, given the corresponding change in degrees of freedom, there was evidence that the three-factor solution from the CFA was invariant across groups.
Multi-Group Analysis Fit Indices by Age, PSA, Hgb and Alkaline Phosphatase Groups by Factor Loading Constraints for the Three-Factor Solution