Table 3.

Results of the single-group and multigroup confirmatory factor analysis of the 16 general colorectal cancer screening items for four race-sex subgroups (n= 1,413) from a colorectal cancer screening intervention trial of primary care patients

Modelnχ2Scaling correction factorMean-adjusted χ2*dfPCFIRMSEA (90% CI)
    White males274176.916171.053940.0000.8920.055 (0.041-0.068)
    White females291182.742154.442940.0000.9140.047 (0.033-0.060)
    Black males195119.91196.601940.4070.9940.012 (0.000-0.040)
    Black females653244.121213.081940.0000.9120.044 (0.036-0.052)
Five-factor and two correlated errors
    White males274126.920123.250920.0160.9560.035 (0.016-0.050)
    White females291141.781121.686920.0210.9580.033 (0.014-0.048)
    Black males195110.25390.348920.5290.9990.000 (0.000-0.037)
    Black females653187.851164.390920.0000.9470.035 (0.026-0.043)
1. Unconstrained1,413566.8091.14497.7153680.0000.9590.016 (0.012-0.019)
2. Equal factor loadings1,413650.2011.19546.7684010.0000.9540.016 (0.012-0.019)
3. Equal factor loadings with rcc_low constraint released1,413614.3801.19518.1203980.0000.9620.015 (0.011-0.018)
Model comparisons
Difference df
Difference test scaling correction factor
Mean-adjusted χ2diff
1 vs 283.392331.7547.6350.048
1 vs 347.571301.7627.0000.623
  • Abbreviations: df, degrees of freedom; scf, scaling correction factor; dtscf, difference test scaling correction factor; RMSEA, root mean square error of approximation.

  • * The mean-adjusted χ2 is used when the outcome variables has a non-normal distribution. Satorra and Bentler (61) showed that if the usual normal-theory χ2 test statistic is divided by a scaling correction factor, the scaled statistic better approximates a χ2 distribution.

  • The difference between two mean-adjusted χ2 for nested models does not follow a χ2 distribution. Satorra and Bentler (66) showed that the following equation for the mean-adjusted difference statistic, which incorporates a difference test scaling correction factor, does follow a χ2 distribution. Mean-adjusted χ2diff = (χ 2nested2nested − χ 2comparison) / dtscf. dtscf = (dfnested × scfnesteddfcomparison × scfcomparison) / (dfnesteddfcomparison).