Skip to main content
. Author manuscript; available in PMC: 2012 Mar 1.
Published in final edited form as: Drug Alcohol Depend. 2011 Mar 1;114(1):41–48. doi: 10.1016/j.drugalcdep.2010.06.023

Table 2.

Step-Wise Development of the Hybrid Latent Growth Model: Preliminary Models and the Final Model, each with Fit Indices

Model RMSEA
(90% CI)		 SRMR AIC CFI TLI χ 2 df Δ χ 2 Δ df
Unconditional Unidimensional Latent Growth Models:
1.1 ASI: Phase-wise1,2 0.068
(0.050 –
0.086)		 0.063 −6473.002 0.941 0.939 64.648*** 20
1.2.1 BDI: Quadratic1,3 0.036
(0.009 –
0.059)		 0.032 −5917.667 0.990 0.988 31.296* 19
1.2.2 BDI: Linear3 0.070
(0.053 –
0.087)		 0.053 −5879.464 0.954 0.958 77.499*** 23 46.203*** 4
Unconditional Unidimensional Hybrid Latent Growth Models with Autoregressive (AR) Effects:
2.1.1 ASI: AR effects freely estimated1,1 0.026
(0.000 –
0.051)		 0.035 −6509.216 0.993 0.991 22.434 17
2.1.2 ASI: AR effects restricted to be equal4 0.041
(0.019 –
0.061)		 0.046 −6501.829 0.977 0.978 39.822* 22 17.388** 5
2.1.3 ASI: AR effects restricted to be zero4 0.073
(0.056 –
0.090)		 0.072 −6461.122 0.922 0.929 82.528*** 23 60.094*** 6
2.2.1 BDI: AR effects freely estimated1,5 0.040
(0.014 –
0.064)		 0.031 −5914.367 0.989 0.986 28.596* 16
2.2.2 BDI: AR effects restricted to be equal5. 0.031
(0.000 –
0.053)		 0.033 −5922.427 0.992 0.992 30.536 21 1.940 5
2.2.3 BDI: AR effects restricted to be zero5 0.036
(0.012 –
0.057)		 0.035 −5918.876 0.988 0.989 36.088* 22 7.492 6
Conditional Multidimensional Hybrid Latent Growth Models with Autoregressive (AR) and Cross-Lagged Effects:
3.1.1 Contemporaneous residual variances
  freely estimated (Unrestricted
  Model)2,2,4,5 		0.029
(0.015 –
0.040)		 0.033 −11127.265 0.984 0.975 123.004* 88
3.1.2 Contemporaneous residual variances
  restricted to be equal2,5,5 		0.026
(0.012 –
0.038)		 0.034 −11136.724 0.985 0.979 125.545* 94 2.541 6
3.1.3 Contemporaneous residual variances
  restricted to be zero3,4,5 		0.051
(0.042 –
0.060)		 0.042 −11049.396 0.944 0.922 214.873*** 95 91.869*** 7
3.2.1 BDI on ASI freely estimated & ASI on
  BDI freely estimated1,2,4,5 		0.026
(0.012 –
0.038)		 0.034 −11136.724 0.985 0.979 125.545* 94
3.2.2 BDI on ASI freely estimated & ASI on
  BDI restricted to be equal2,4,5 		0.028
(0.015 –
0.039)		 0.037 −11135.226 0.982 0.976 137.043** 99 11.498* 5
3.2.3 BDI on ASI freely estimated & ASI on
  BDI restricted to be zero2,4,5 		0.028
(0.015 –
0.039)		 0.037 −11136.751 0.982 0.977 137.518** 100 11.973 6
3.2.4 BDI on ASI restricted to be equal &
  ASI on BDI freely estimated2,4,5 		– 6 – 6 – 6 – 6 – 6 – 6 – 6 – 6 – 6
3.2.5 BDI on ASI restricted to be equal &
  ASI on BDI restricted to be equal2,4,1 		0.028
(0.015 –
0.038)		 0.040 −11139.635 0.982 0.977 142.635** 104 17.090 10
3.2.6 BDI on ASI restricted to be equal &
  ASI on BDI restricted to be zero2,4,5 		0.027
(0.015 –
0.038)		 0.040 −11140.925 0.982 0.977 143.344** 105 17.799 11
3.2.7 BDI on ASI restricted to be zero &
  ASI on BDI freely estimated2,4,5 		0.030
(0.018 –
0.040)		 0.038 −11130.711 0.980 0.973 143.559** 100 18.014** 6
3.2.8 BDI on ASI restricted to be zero &
  ASI on BDI restricted to be equal2,4,5 		0.030
(0.019 –
0.041)		 0.041 −11131.704 0.978 0.972 152.565** 105 27.020** 11
3.2.9 BDI on ASI restricted to be zero &
  ASI on BDI restricted to be zero2,4,5 		0.030
(0.019 –
0.040)		 0.041 −11133.241 0.978 0.972 153.028** 106 27.483** 12

Note. ASI = Addiction Severity Index–Drug Use Composite score; BDI = Beck Depression Inventory; RMSEA = root-mean-square error of approximation; CI = confidence interval; SRMR = standardized root-mean-square residual; AIC = Akaike information criterion; CFI = comparative fit index; TLI = Tucker-Lewis index.

1

Model was used as reference for the evaluation of more restricted models within the respective modeling step.

2

The covariance of the intercept and of the slope of change during months 0 to 1 was fixed to be zero due to convergence problems.

3

Data were not available for 2 patients.

4

The residual variance of the slope of change during months 2 to 6 was fixed to be zero due to convergence problems.

5

The residual variance of the quadratic growth parameter was fixed to be zero due to convergence problems.

6

The model estimation did not converge indicating that the model does not fit the data.

*

p < .05

**

p < .01

***

p < .001.