Moderator analysis using OSMASEM
hansol6461
Joined: 02/17/2021
Dear Professor Cheung,
I am writing this post to seek your help regarding the OSMASEM. Building a model with no moderator works just fine, but adding a moderator to the model does not work properly. I am currently learning the OSMASEM approach by replicating one of the published articles that applied the approach, entitled “Simple View of Reading in Chinese: A One-Stage Meta-Analytic Structural Equation Modeling” written by Peng and his colleagues (https://journals.sagepub.com/doi/abs/10.3102/0034654320964198). Thanks to their open data (Appendix C), I was able to construct a dataset and to replicate their first model with no moderator by computing the same coefficients and p-values in accordance with the figure in the article. However, when I add a moderator, the results are unstable—seemingly inaccurate (very large) standard errors. It would be appreciated if you could kindly review my codes.
Thank you in advance.
Rerunning the model again may
Rerunning the model again may help. As you can see, Tau1_2 vecTau1 and Tau1_2vecTau7 are very negative meaning that Tau2_2 and Tau2_7 are very close to 0. Thus, their SEs are large.
> fit1 <- rerun(fit1, autofixtau2=TRUE)
> summary(fit1)
Summary of With moderator
free parameters:
name matrix row col Estimate Std.Error A z value Pr(>|z|)
1 d1 A0 FLUEN DECOD 0.64691401 0.02414233 26.79584434 0.000000e+00
2 d2 A0 ACCU DECOD 0.79586209 0.02800738 28.41615808 0.000000e+00
3 decod2rc A0 RC DECOD 0.25559757 0.15223900 1.67892310 9.316703e-02
4 l1 A0 VOC LANG 0.67867804 0.04546883 14.92622655 0.000000e+00
5 l2 A0 LC LANG 0.70264701 0.05247982 13.38889867 0.000000e+00
6 lang2rc A0 RC LANG 0.50301585 0.14690273 3.42414233 6.167431e-04
7 m1 A0 PA META 0.62209060 0.01723119 36.10259065 0.000000e+00
8 m2 A0 RAN META -0.65364225 0.02191765 -29.82263878 0.000000e+00
9 m3 A0 MOR META 0.67728289 0.01746958 38.76927928 0.000000e+00
10 m4 A0 OTH META 0.60776956 0.02094887 29.01204995 0.000000e+00
11 meta2decod A0 DECOD META 0.75596660 0.03195421 23.65780847 0.000000e+00
12 langWITHdecod S0 LANG DECOD 0.17921498 0.05238822 3.42090245 6.241372e-04
13 metaWITHlang S0 META LANG 0.80828780 0.04977277 16.23955760 0.000000e+00
14 decod2rc_1 A1 RC DECOD 0.73925653 0.33281239 2.22124101 2.633464e-02
15 lang2rc_1 A1 RC LANG -0.57797377 0.34915800 -1.65533591 9.785638e-02
16 meta2decod_1 A1 DECOD META -0.03813199 0.03933175 -0.96949637 3.322976e-01
17 Tau1_1 vecTau1 1 1 -1.81314766 0.13693723 -13.24072059 0.000000e+00
18 Tau1_2 vecTau1 2 1 -14.98088083 533.33995428 -0.02808880 9.775913e-01
19 Tau1_3 vecTau1 3 1 -1.99834193 0.57103760 -3.49949273 4.661443e-04
20 Tau1_4 vecTau1 4 1 -2.47809594 0.30878608 -8.02528394 1.110223e-15
21 Tau1_5 vecTau1 5 1 -2.10233487 0.24638746 -8.53263747 0.000000e+00
22 Tau1_6 vecTau1 6 1 -1.66980132 0.23848381 -7.00173862 2.527978e-12
23 Tau1_7 vecTau1 7 1 -19.35168647 719.49985513 -0.02689603 9.785427e-01
24 Tau1_8 vecTau1 8 1 -1.79439962 0.34151843 -5.25418090 1.486847e-07
25 Tau1_9 vecTau1 9 1 -1.72923582 0.10588546 -16.33119189 0.000000e+00
26 Tau1_10 vecTau1 10 1 -1.86758996 0.23176991 -8.05794830 6.661338e-16
27 Tau1_11 vecTau1 11 1 -2.20455890 0.13765525 -16.01507360 0.000000e+00
28 Tau1_12 vecTau1 12 1 -1.84738284 0.08228960 -22.44977271 0.000000e+00
29 Tau1_13 vecTau1 13 1 -2.18570462 0.13073873 -16.71811167 0.000000e+00
30 Tau1_14 vecTau1 14 1 -2.27474296 0.11394564 -19.96340539 0.000000e+00
31 Tau1_15 vecTau1 15 1 -1.71508022 0.10308624 -16.63733456 0.000000e+00
32 Tau1_16 vecTau1 16 1 -1.02500263 0.21794995 -4.70292671 2.564585e-06
33 Tau1_17 vecTau1 17 1 -1.76588992 0.14591155 -12.10246823 0.000000e+00
34 Tau1_18 vecTau1 18 1 -1.46397359 0.10443147 -14.01851011 0.000000e+00
35 Tau1_19 vecTau1 19 1 -1.26264618 0.14858137 -8.49801136 0.000000e+00
36 Tau1_20 vecTau1 20 1 -1.59642517 0.11088963 -14.39652335 0.000000e+00
37 Tau1_21 vecTau1 21 1 -1.17345377 0.15721534 -7.46399010 8.393286e-14
38 Tau1_22 vecTau1 22 1 -1.79465560 0.21934346 -8.18194270 2.220446e-16
39 Tau1_23 vecTau1 23 1 -1.17846134 0.24015095 -4.90716911 9.240036e-07
40 Tau1_24 vecTau1 24 1 -1.05133842 0.25949778 -4.05143506 5.090446e-05
41 Tau1_25 vecTau1 25 1 -2.19769306 0.32907430 -6.67840990 2.415490e-11
42 Tau1_26 vecTau1 26 1 -2.37704162 0.43782954 -5.42914853 5.662355e-08
43 Tau1_27 vecTau1 27 1 -1.82992444 0.15172991 -12.06040652 0.000000e+00
44 Tau1_28 vecTau1 28 1 -1.87120779 0.21916385 -8.53794010 0.000000e+00
45 Tau1_29 vecTau1 29 1 -2.27618820 0.14399584 -15.80731966 0.000000e+00
46 Tau1_30 vecTau1 30 1 -2.46765302 0.28959601 -8.52101874 0.000000e+00
47 Tau1_31 vecTau1 31 1 -1.81074322 0.11445191 -15.82099582 0.000000e+00
48 Tau1_32 vecTau1 32 1 -1.68012285 0.08742181 -19.21857778 0.000000e+00
49 Tau1_33 vecTau1 33 1 -1.52835159 0.09914218 -15.41575476 0.000000e+00
50 Tau1_34 vecTau1 34 1 -1.49870425 0.12893648 -11.62358597 0.000000e+00
51 Tau1_35 vecTau1 35 1 -1.68146848 0.15237981 -11.03471935 0.000000e+00
52 Tau1_36 vecTau1 36 1 -1.83791285 0.13210364 -13.91265870 0.000000e+00
Model Statistics:
| Parameters | Degrees of Freedom | Fit (-2lnL units)
Model: 52 1166 -724.0495
Saturated: 702 516 NA
Independence: 72 1146 NA
Number of observations/statistics: 49132/1218
Information Criteria:
| df Penalty | Parameters Penalty | Sample-Size Adjusted
AIC: -3056.049 -620.0495 -619.9372
BIC: -13319.491 -162.3316 -327.5883
To get additional fit indices, see help(mxRefModels)
timestamp: 2021-02-27 18:03:50
Wall clock time: 70.233 secs
OpenMx version number: 2.18.1
Need help? See help(mxSummary)
> diag(VarCorr(fit1))
Tau2_1 Tau2_2 Tau2_3 Tau2_4 Tau2_5 Tau2_6 Tau2_7 Tau2_8
2.661460e-02 9.722372e-14 1.837648e-02 7.039685e-03 1.492571e-02 3.545104e-02 1.553598e-17 2.763149e-02
Tau2_9 Tau2_10 Tau2_11 Tau2_12 Tau2_13 Tau2_14 Tau2_15 Tau2_16
3.147783e-02 2.386888e-02 1.216591e-02 2.485328e-02 1.263342e-02 1.057264e-02 3.238174e-02 1.287342e-01
Tau2_17 Tau2_18 Tau2_19 Tau2_20 Tau2_21 Tau2_22 Tau2_23 Tau2_24
2.925280e-02 5.350677e-02 8.003491e-02 4.105468e-02 9.566454e-02 2.761735e-02 9.471123e-02 1.221291e-01
Tau2_25 Tau2_26 Tau2_27 Tau2_28 Tau2_29 Tau2_30 Tau2_31 Tau2_32
1.233412e-02 8.616440e-03 2.573640e-02 2.369679e-02 1.054212e-02 7.188261e-03 2.674290e-02 3.472673e-02
Tau2_33 Tau2_34 Tau2_35 Tau2_36
4.704253e-02 4.991626e-02 3.463339e-02 2.532848e-02
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In reply to Rerunning the model again may by Mike Cheung
A follow-up question regarding R2 for moderation
Dear Professor Cheung,
I truly appreciate your feedback. It works just fine! I am very delighted to be able to move forward to next learning steps and want to ask one more favor with the following last question: How do I label the computed 36 Tau2s to understand the results of R2 for moderation (osmasemR2)? Given that my RAM$A0 is a 12*12 matrix, I first guessed there should be 66 Taus. Actually, there are 36 Tau2s coming from the osmasemR2 command and this made me confused. Do I have a 9*9 matrix? When I read MASEM on Nohe et al. (2015) data, it seems that your 6 Tau2s exactly correspond to the lower diagonal elements of a 4*4 matrix with w1,s1,w2,s2 in accordance with the structure of RAM$A0. My best understanding is that this pattern does not apply to my case where both observed and latent variables are involved. When it comes to coefficients, I have their names; however, I am clueless with nameless Tau2s. I look forward to hearing from you, sir.
Thank you very much.
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In reply to A follow-up question regarding R2 for moderation by hansol6461
I could not edit the added comment.
Please disregard this message and see the following comment. Thank you.
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A follow-up question regarding R2 for moderation
Dear Professor Cheung,
I truly appreciate your feedback. It works just fine! I am very delighted to be able to move forward to next learning steps and want to ask one more favor with the following last question: How do I label the computed 36 Tau2s to understand the results of R2 for moderation (osmasemR2)? Given that my A0 is a 12X12 matrix, I first guessed there should be 66 Taus (i.e., 66 lower diagonal elements). Actually, there are 36 Tau2s from the osmasemR2 command and this made me confused. Do I have a 9X9 matrix? When I read MASEM on Nohe et al. (2015) data, it seems that your 6 Tau2s exactly correspond to the lower diagonal elements of a 4X4 matrix with w1,s1,w2,s2 in accordance with the structure of A0. My best understanding is that this pattern does not apply to my case where both observed and latent variables are involved. When it comes to coefficients, I have their names; however, I am clueless with Tau2s with no labels. I look forward to hearing from you, sir.
Thank you very much.
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As indicated in Equation (1)
As indicated in Equation (1) in Jak and Cheung (2020), the random effects Tau^2 are on the correlation coefficients, not on the SEM parameters. In your data, there are 9 variables. Thus, 9*8/2=36 Tau^2 on the correlation coefficients. It may not be easy to interpret the R^2 in such a model.
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