TABLE 4.
Assessment of measurement invariance of the PHQ-9 and GAD-7 across demographic subgroups, over time and status of diabetes.
| PHQ-9 | Items constrained | χ 2 | df | p | CFI | RMSEA | SRMR | Δχ 2 | p | Δ CFI | Δ RMSEA | Δ SRMR | |
| Gender | Configural | 122.124 | 52 | <0.001 | 0.945 | 0.063 | 0.039 | − | − | − | − | − | |
| Metric | 121.398 | 59 | <0.001 | 0.948 | 0.057 | 0.043 | 3.666 | 0.817 | 0.004 | –0.006 | 0.004 | ||
| Scalar | 131.714 | 66 | <0.001 | 0.948 | 0.054 | 0.044 | 8.101 | 0.324 | –0.001 | –0.003 | 0.001 | ||
| Factor variance | 137.501 | 68 | <0.001 | 0.944 | 0.056 | 0.069 | 5.047 | 0.080 | –0.004 | 0.001 | 0.025 | ||
| Residual* | 191.250 | 75 | <0.001 | 0.894 | 0.072 | 0.069 | 39.371 | <0.001 | –0.054 | 0.018 | 0.025 | ||
| Partial residual* | 2,6,7 | 142.568 | 72 | <0.001 | 0.941 | 0.055 | 0.052 | 11.250 | 0.081 | –0.007 | 0.001 | 0.007 | |
| Age | Configural | 176.513 | 78 | <0.001 | 0.932 | 0.072 | 0.044 | − | − | − | − | − | |
| Metric | 177.109 | 92 | <0.001 | 0.935 | 0.065 | 0.055 | 114.809 | 0.648 | 0.003 | –0.007 | 0.011 | ||
| Scalar | 198.213 | 106 | <0.001 | 0.934 | 0.061 | 0.057 | 172.130 | 0.245 | –0.001 | –0.004 | 0.002 | ||
| Factor var | 209.552 | 110 | <0.001 | 0.927 | 0.063 | 0.084 | 98.314 | 0.043 | –0.007 | 0.002 | 0.027 | ||
| Residual* | 208.579 | 124 | <0.001 | 0.928 | 0.059 | 0.069 | 21.647 | 0.248 | –0.006 | –0.002 | 0.012 | ||
| Education | Configural | 156.348 | 78 | <0.001 | 0.941 | 0.064 | 0.043 | − | − | − | − | − | |
| Metric | 186.644 | 92 | <0.001 | 0.926 | 0.066 | 0.063 | 29.826 | 0.008 | –0.016 | 0.002 | 0.020 | ||
| Partial metric | 7 | 167.316 | 90 | <0.001 | 0.940 | 0.060 | 0.052 | 13.392 | 0.341 | –0.001 | –0.004 | 0.009 | |
| Scalar | 185.049 | 104 | <0.001 | 0.941 | 0.055 | 0.053 | 12.461 | 0.569 | 0.001 | –0.004 | 0.001 | ||
| Factor variance | 218.204 | 108 | <0.001 | 0.916 | 0.065 | 0.110 | 19.521 | <0.001 | –0.025 | 0.009 | 0.057 | ||
| Residual* | 274.559 | 122 | <0.001 | 0.859 | 0.079 | 0.109 | 58.147 | <0.001 | –0.082 | 0.023 | 0.056 | ||
| Partial residual* | 6,7 | 200.944 | 118 | <0.001 | 0.932 | 0.056 | 0.064 | 20.026 | 0.129 | –0.009 | 0.000 | 0.012 | |
| T2D status | Configural | 131.678 | 52 | <0.001 | 0.946 | 0.064 | 0.038 | − | − | − | − | − | |
| Metric | 130.505 | 59 | <0.001 | 0.948 | 0.060 | 0.044 | 58.489 | 0.558 | 0.001 | –0.005 | 0.006 | ||
| Scalar | 139.259 | 66 | <0.001 | 0.949 | 0.056 | 0.044 | 43.797 | 0.735 | 0.001 | –0.004 | 0.000 | ||
| Factor variance | 136.175 | 68 | <0.001 | 0.951 | 0.054 | 0.049 | 0.8415 | 0.657 | 0.002 | –0.002 | 0.005 | ||
| Residual* | 144.056 | 75 | <0.001 | 0.945 | 0.054 | 0.050 | 11.655 | 0.233 | –0.004 | –0.001 | 0.006 | ||
| Time | Configural | 173.821 | 78 | <0.001 | 0.968 | 0.050 | 0.033 | − | − | − | − | − | |
| Metric | 197.636 | 92 | <0.001 | 0.963 | 0.049 | 0.046 | 24.934 | 0.035 | –0.005 | –0.001 | 0.013 | ||
| Scalar | 247.699 | 106 | <0.001 | 0.954 | 0.051 | 0.049 | 67.865 | <0.001 | –0.009 | 0.002 | 0.003 | ||
| Factor vriance | 255.133 | 110 | <0.001 | 0.952 | 0.051 | 0.063 | 7.928 | 0.094 | –0.002 | 0.000 | 0.014 | ||
| Residual* | 489.852 | 124 | <0.001 | 0.845 | 0.086 | 0.102 | 127.070 | <0.001 | –0.109 | 0.035 | 0.054 | ||
| Partial residual* | 1,2,5,6,7,8 | 144.056 | 112 | <0.001 | 0.945 | 0.054 | 0.050 | 15.264 | 0.018 | 0.009 | –0.003 | –0.003 | |
| Gender | Configural | 45.472 | 24 | 0.005 | 0.987 | 0.053 | 0.025 | − | − | − | − | − | |
| Metric | 46.633 | 30 | 0.027 | 0.990 | 0.043 | 0.033 | 27.551 | 0.839 | 0.002 | –0.010 | 0.008 | ||
| Scalar | 64.176 | 36 | 0.003 | 0.984 | 0.049 | 0.040 | 230.732 | <0.001 | –0.006 | 0.006 | 0.008 | ||
| Factor variance | 88.158 | 37 | <0.001 | 0.970 | 0.065 | 0.136 | 162.348 | <0.001 | –0.014 | 0.017 | 0.095 | ||
| Residual* | 131.510 | 43 | <0.001 | 0.941 | 0.085 | 0.073 | 45.674 | <0.001 | –0.042 | 0.036 | 0.032 | ||
| Partial residual* | 2,7 | 66.057 | 41 | 0.013 | 0.986 | 0.042 | 0.039 | 15.748 | 0.008 | –0.010 | 0.010 | 0.009 | |
| Age | Configural | 63.391 | 36 | 0.003 | 0.986 | 0.057 | 0.027 | − | − | − | − | − | |
| Metric | 75.737 | 48 | 0.007 | 0.985 | 0.051 | 0.049 | 134.609 | 0.336 | –0.001 | –0.006 | 0.022 | ||
| Scalar | 95.195 | 60 | 0.003 | 0.983 | 0.049 | 0.052 | 198.170 | 0.071 | –0.002 | –0.002 | 0.003 | ||
| Factor variance | 95.908 | 62 | 0.004 | 0.983 | 0.048 | 0.064 | 18.565 | 0.395 | 0.000 | –0.001 | 0.011 | ||
| Residual* | 101.703 | 74 | 0.018 | 0.985 | 0.042 | 0.053 | 11.880 | 0.616 | 0.002 | –0.007 | 0.001 | ||
| Education | Configural | 66.657 | 36 | 0.001 | 0.984 | 0.060 | 0.026 | − | − | − | − | − | |
| Metric | 83.912 | 48 | 0.001 | 0.980 | 0.059 | 0.050 | 183.622 | 0.105 | –0.005 | –0.001 | 0.024 | ||
| Scalar | 110.261 | 60 | <0.001 | 0.974 | 0.060 | 0.053 | 301.806 | 0.003 | –0.005 | 0.000 | 0.003 | ||
| Factor variance | 120.791 | 62 | <0.001 | 0.969 | 0.064 | 0.100 | 75.149 | 0.023 | –0.005 | 0.005 | 0.046 | ||
| Residual* | 123.384 | 74 | <0.001 | 0.971 | 0.057 | 0.065 | 17.481 | 0.231 | –0.003 | –0.003 | 0.011 | ||
| T2D status | Configural | 40.073 | 24 | 0.021 | 0.991 | 0.046 | 0.023 | − | − | − | − | − | |
| Metric | 42.627 | 30 | 0.063 | 0.992 | 0.038 | 0.029 | 42.037 | 0.649 | 0.001 | –0.008 | 0.006 | ||
| Scalar | 50.677 | 36 | 0.053 | 0.992 | 0.036 | 0.030 | 76.128 | 0.268 | 0.000 | –0.002 | 0.001 | ||
| Factor variance | 50.969 | 37 | 0.063 | 0.992 | 0.035 | 0.038 | 0.693 | 0.405 | 0.000 | –0.001 | 0.008 | ||
| Residual* | 66.057 | 43 | 0.013 | 0.986 | 0.042 | 0.039 | 14.072 | 0.050 | –0.006 | 0.007 | 0.008 | ||
| Time | Configural | 84.234 | 36 | <0.001 | 0.988 | 0.051 | 0.022 | − | − | − | − | − | |
| Metric | 94.655 | 48 | <0.001 | 0.988 | 0.044 | 0.032 | 11.560 | 0.482 | 0.000 | –0.007 | 0.010 | ||
| Scalar | 135.387 | 60 | <0.001 | 0.982 | 0.048 | 0.038 | 54.319 | <0.001 | –0.006 | 0.003 | 0.005 | ||
| Factor variance | 149.413 | 62 | <0.001 | 0.979 | 0.051 | 0.074 | 9.799 | 0.007 | –0.003 | 0.004 | 0.036 | ||
| Residual* | 210.355 | 74 | <0.001 | 0.964 | 0.061 | 0.058 | 61.287 | <0.001 | –0.018 | 0.013 | 0.021 | ||
| Partial residual* | 4,5 | 66.057 | 70 | 0.013 | 0.986 | 0.042 | 0.039 | 14.077 | 0.170 | –0.001 | –0.002 | 0.003 | |
df, degrees of freedom; Δχ2, change in χ2; CFI, comparative fit index; RMSEA, root-mean-square error of approximation; SRMR, standardized root mean square residual: ΔCFI, change in CFI; ΔRMSEA, change in RMSEA; ΔSRMR, change in SRMR; T2D, type two diabetes. *Compared to the model with constrained loadings and intercepts (i.e., the scalar invariant model).