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Satorra-Bentler (2001) Scaled Difference Chi-Square Test for Mplus
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Based on Kline (2016) Topic Box 12.2
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and Mplus Guidance (https://www.statmodel.com/chidiff.shtml; https://stats.idre.ucla.edu/mplus/faq/how-can-i-compute-a-chi-square-test-for-nested-models-with-the-mlr-or-mlm-estimators/ )
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Hinson and Utke (2021) uses MLR estimation. The approach outlined here works for MLR and some, but not all,
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other types of estimation. See the Mplus Guidance for details.
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Baseline (complex/less restrictive) model = more estimated parameters (SMALLER df)
EQ-VD Model
(M or H0)
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Nested (simpler/more restrictive) comparison model = fewer estimated parameters (LARGER df)
EQ or VD Model
(M or H1)
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= inputs (i.e., input your study's values into these cells only)
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EQ
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Output from Mplus (v7): (all direct Mplus output is italicized)
Nested (1)
Baseline
Computation
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Chi-Square Test of Model Fit
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Value(aka: "X2_SB")1636.0541451.766
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Degrees of Freedom(aka: "df")5048
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P-Value00
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Scaling Correction Factor for MLR(aka: "c")1.58781.5793
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Adjust X2_SB(aka: "X2_SB_adj")2597.7265412292.774044
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Diff in Chi-Sq (Xd)
X2_SB_Adj_nested - X2_SB_Adj_baseline
304.9524974
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Diff in df (DFd)
df_nested - df_baseline
2
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cd
(c_nested*df_nested - c_baseline*df_baseline)/(DFd)
1.7918
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Scaled Chi-Sq Diff(Xd/cd)170.1933795
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p-value (testing null of equal fit across models)
 -
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(1)Nested models are generally created by taking a baseline model and dropping paths. Our EQ and VD Models are not exactly nested because the EQ-VD Model includes additional factors. Thus, we re-estimate the EQ and VD models within the EQ-VD model after fixing either both VD or both EQ paths to 0. This leads to 2 additional free parameters in the nested model. Specifically, to get the EQ Nested Model used here, we fix the direct and indirect VD paths at 0.
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Alternative Method: Using Likelihood Ratios
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Number of Free Parameters
(aka: "PARM")4042
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Loglikelihood
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H0 Value(aka: "LL")73528.15573680.665
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H0 Scaling Correction Factor for MLR
(aka: "c")5.28585.1194
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Diff in Parameters Estimated (PARMd)
PARM_nested - PARM_baseline
-2
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diff
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cd
(c_nested*PARM_nested - c_baseline*PARM_baseline)/(PARMd)
1.79140.0004
(similar to above, diff = rounding)
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Test Statistic
-2*(LL_nested - LL_baseline)/cd
170.2690633-0.0756837958
(similar to above, diff = rounding)
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p-value (testing null of equal fit across models)
 -
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