Dear Statalist users,
I am going to estimate a sem model with several covariates, and wanted to check for possible collinearity problems. I used the collin (by Phil Ender) and got the following output (all log* variables are exposure variables of interest, the rest is covariates):
As you can see, the VIFs seem not to indicate problems, but the condition number is very high, and seems to indicate collinearity problems. Dropping the intercept, however, lowers the condition number to an acceptable level:
When I do the sem analysis, I get the following results, including model fit:
Do I have reason to be concerned about multicollinearity?
Best regards,
Kjell
I am going to estimate a sem model with several covariates, and wanted to check for possible collinearity problems. I used the collin (by Phil Ender) and got the following output (all log* variables are exposure variables of interest, the rest is covariates):
Code:
collin logAs logCo logK_ug logCd logCs logCu logHg logMn logMo logPb logSe logZn logMg_ug logNa_ug Maternal_age Maternal_edu Parity MADHD_SS TOTAL_Fish_Intake if PP_ADHD_SS!=.
Collinearity Diagnostics
SQRT R-
Variable VIF VIF Tolerance Squared
----------------------------------------------------
logAs 1.47 1.21 0.6819 0.3181
logCo 1.22 1.10 0.8215 0.1785
logK_ug 2.07 1.44 0.4840 0.5160
logCd 1.25 1.12 0.8012 0.1988
logCs 1.25 1.12 0.7969 0.2031
logCu 1.37 1.17 0.7289 0.2711
logHg 1.76 1.33 0.5696 0.4304
logMn 1.26 1.12 0.7909 0.2091
logMo 1.16 1.08 0.8641 0.1359
logPb 1.26 1.12 0.7918 0.2082
logSe 1.32 1.15 0.7556 0.2444
logZn 1.59 1.26 0.6303 0.3697
logMg_ug 1.68 1.30 0.5949 0.4051
logNa_ug 1.47 1.21 0.6809 0.3191
Maternal_age 1.28 1.13 0.7817 0.2183
Maternal_edu 1.18 1.08 0.8497 0.1503
Parity 1.23 1.11 0.8146 0.1854
MADHD_SS 1.05 1.02 0.9552 0.0448
TOTAL_Fish_Intake 1.15 1.07 0.8732 0.1268
----------------------------------------------------
Mean VIF 1.37
Cond
Eigenval Index
---------------------------------
1 15.8980 1.0000
2 1.3086 3.4855
3 0.8965 4.2111
4 0.6585 4.9134
5 0.3864 6.4144
6 0.2504 7.9683
7 0.1637 9.8558
8 0.1233 11.3536
9 0.0937 13.0223
10 0.0875 13.4817
11 0.0528 17.3523
12 0.0306 22.7821
13 0.0281 23.7791
14 0.0199 28.2944
15 0.0011 118.0879
16 0.0005 183.6459
17 0.0002 261.0906
18 0.0001 491.0595
19 0.0000 834.7926
20 0.0000 946.2107
---------------------------------
Condition Number 946.2107
Eigenvalues & Cond Index computed from scaled raw sscp (w/ intercept)
Det(correlation matrix) 0.0425
Code:
collin logAs logCo logK_ug logCd logCs logCu logHg logMn logMo logPb logSe logZn logMg_ug logNa_ug Maternal_age Maternal_edu Parity MADHD_SS TOTAL_Fish_Intake if PP_ADHD_SS!=., corr
Cond
Eigenval Index
---------------------------------
1 2.9785 1.0000
2 2.0193 1.2145
3 1.5783 1.3737
4 1.4891 1.4143
5 1.2766 1.5275
6 1.1341 1.6206
7 1.0118 1.7158
8 0.9726 1.7500
9 0.8092 1.9186
10 0.7914 1.9400
11 0.7275 2.0233
12 0.7138 2.0428
13 0.6610 2.1228
14 0.6043 2.2201
15 0.5528 2.3212
16 0.5022 2.4353
17 0.4795 2.4924
18 0.3994 2.7307
19 0.2984 3.1591
---------------------------------
Condition Number 3.1591
Eigenvalues & Cond Index computed from deviation sscp (no intercept)
Det(correlation matrix) 0.0425
Code:
Endogenous variables
Observed: THYREOIDEA BARN_DNA_1606 PP_ADHD_SS
Exogenous variables
Observed: logCd logCo logAs TOTAL_Fish_Intake Maternal_age Maternal_edu Parity MADHD_SS
Fitting target model:
Iteration 0: log likelihood = -12697.629
Iteration 1: log likelihood = -12697.629
Structural equation model Number of obs = 782
Estimation method = ml
Log likelihood = -12697.629
----------------------------------------------------------------------------------------------------
| OIM
Standardized | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-----------------------------------+----------------------------------------------------------------
Structural |
THYREOIDEA |
logCd | -.0407465 .0357893 -1.14 0.255 -.1108923 .0293992
logCo | .0390415 .03579 1.09 0.275 -.0311055 .1091886
logAs | .0590727 .0355923 1.66 0.097 -.0106869 .1288322
_cons | .1299296 .131326 0.99 0.322 -.1274646 .3873237
---------------------------------+----------------------------------------------------------------
BARN_DNA_1606 |
logCd | .0576503 .0357198 1.61 0.107 -.0123592 .1276599
logCo | -.0774175 .0356707 -2.17 0.030 -.1473308 -.0075042
logAs | -.011075 .0356121 -0.31 0.756 -.0808735 .0587235
_cons | 1.471542 .1375627 10.70 0.000 1.201924 1.74116
---------------------------------+----------------------------------------------------------------
PP_ADHD_SS |
THYREOIDEA | -.015188 .0346469 -0.44 0.661 -.0830946 .0527187
BARN_DNA_1606 | -.0171873 .0346506 -0.50 0.620 -.0851012 .0507266
logCd | .0038546 .0355215 0.11 0.914 -.0657664 .0734755
logCo | .0847461 .0350729 2.42 0.016 .0160044 .1534877
logAs | .0443859 .0359332 1.24 0.217 -.026042 .1148137
TOTAL_Fish_Intake | .0196385 .0355246 0.55 0.580 -.0499885 .0892655
Maternal_age | -.0692916 .0372963 -1.86 0.063 -.142391 .0038078
Maternal_edu | -.1573542 .0361577 -4.35 0.000 -.228222 -.0864865
Parity | .0574914 .0372399 1.54 0.123 -.0154975 .1304804
MADHD_SS | .1504165 .0346772 4.34 0.000 .0824505 .2183825
_cons | 1.307863 .288134 4.54 0.000 .7431304 1.872595
-----------------------------------+----------------------------------------------------------------
mean(logCd)| -2.218876 .0665337 -33.35 0.000 -2.34928 -2.088472
mean(logCo)| -2.910331 .0818192 -35.57 0.000 -3.070693 -2.749968
mean(logAs)| .4790394 .0377558 12.69 0.000 .4050395 .5530394
mean(TOTAL_Fish_Intake)| 1.541774 .0529021 29.14 0.000 1.438088 1.64546
mean(Maternal_age)| 4.88355 .1285595 37.99 0.000 4.631578 5.135522
mean(Maternal_edu)| 2.773015 .0787109 35.23 0.000 2.618745 2.927286
mean(Parity)| .723081 .0401631 18.00 0.000 .6443628 .8017992
mean(MADHD_SS)| 3.80549 .1026558 37.07 0.000 3.604289 4.006692
-----------------------------------+----------------------------------------------------------------
var(e.THYREOIDEA)| .9936511 .0056625 .9826145 1.004812
var(e.BARN_DNA_1606)| .9914212 .0065675 .9786324 1.004377
var(e.PP_ADHD_SS)| .9260464 .0180988 .8912443 .9622076
var(logCd)| 1 . . .
var(logCo)| 1 . . .
var(logAs)| 1 . . .
var(TOTAL_Fish_Intake)| 1 . . .
var(Maternal_age)| 1 . . .
var(Maternal_edu)| 1 . . .
var(Parity)| 1 . . .
var(MADHD_SS)| 1 . . .
-----------------------------------+----------------------------------------------------------------
cov(e.THYREOIDEA,e.BARN_DNA_1606)| -.0144893 .0357524 -0.41 0.685 -.0845627 .0555842
cov(logCd,logCo)| .0967001 .0354255 2.73 0.006 .0272674 .1661329
cov(logCd,logAs)| .017203 .0357493 0.48 0.630 -.0528644 .0872704
cov(logCd,TOTAL_Fish_Intake)| .086831 .0354903 2.45 0.014 .0172712 .1563907
cov(logCd,Maternal_age)| .0803381 .0355291 2.26 0.024 .0107023 .1499739
cov(logCd,Maternal_edu)| -.132176 .0351352 -3.76 0.000 -.2010397 -.0633123
cov(logCd,Parity)| .145757 .0350002 4.16 0.000 .0771579 .2143561
cov(logCd,MADHD_SS)| -.0195149 .0357463 -0.55 0.585 -.0895763 .0505466
cov(logCo,logAs)| .014158 .0357528 0.40 0.692 -.0559162 .0842321
cov(logCo,TOTAL_Fish_Intake)| .0609902 .0356269 1.71 0.087 -.0088372 .1308177
cov(logCo,Maternal_age)| .0545553 .0356535 1.53 0.126 -.0153242 .1244349
cov(logCo,Maternal_edu)| .0246906 .0357381 0.69 0.490 -.0453548 .0947361
cov(logCo,Parity)| .1501533 .0349537 4.30 0.000 .0816453 .2186612
cov(logCo,MADHD_SS)| .0527544 .0356604 1.48 0.139 -.0171387 .1226475
cov(logAs,TOTAL_Fish_Intake)| .1952887 .0343961 5.68 0.000 .1278736 .2627039
cov(logAs,Maternal_age)| .1267407 .0351855 3.60 0.000 .0577783 .195703
cov(logAs,Maternal_edu)| .194003 .034414 5.64 0.000 .1265527 .2614532
cov(logAs,Parity)| -.0288601 .0357301 -0.81 0.419 -.0988899 .0411697
cov(logAs,MADHD_SS)| -.0406803 .0357007 -1.14 0.255 -.1106525 .0292918
cov(TOTAL_Fish_Intake,Maternal_age)| .1012197 .0353936 2.86 0.004 .0318496 .1705898
cov(TOTAL_Fish_Intake,Maternal_edu)| .1006808 .0353974 2.84 0.004 .0313031 .1700585
cov(TOTAL_Fish_Intake,Parity)| .0791338 .035536 2.23 0.026 .0094845 .148783
cov(TOTAL_Fish_Intake,MADHD_SS)| -.0542005 .0356549 -1.52 0.128 -.1240827 .0156818
cov(Maternal_age,Maternal_edu)| .1586736 .0348596 4.55 0.000 .09035 .2269971
cov(Maternal_age,Parity)| .3200286 .0320975 9.97 0.000 .2571188 .3829385
cov(Maternal_age,MADHD_SS)| -.092296 .0354553 -2.60 0.009 -.1617871 -.0228049
cov(Maternal_edu,Parity)| -.0491163 .0356737 -1.38 0.169 -.1190354 .0208028
cov(Maternal_edu,MADHD_SS)| -.1547283 .0349038 -4.43 0.000 -.2231385 -.0863181
cov(Parity,MADHD_SS)| .0030596 .0357596 0.09 0.932 -.0670279 .0731471
----------------------------------------------------------------------------------------------------
LR test of model vs. saturated: chi2(10) = 10.16, Prob > chi2 = 0.4266
estat gof, stats(all)
----------------------------------------------------------------------------
Fit statistic | Value Description
---------------------+------------------------------------------------------
Likelihood ratio |
chi2_ms(10) | 10.160 model vs. saturated
p > chi2 | 0.427
chi2_bs(27) | 81.775 baseline vs. saturated
p > chi2 | 0.000
---------------------+------------------------------------------------------
Population error |
RMSEA | 0.005 Root mean squared error of approximation
90% CI, lower bound | 0.000
upper bound | 0.039
pclose | 0.993 Probability RMSEA <= 0.05
---------------------+------------------------------------------------------
Information criteria |
AIC | 25529.258 Akaike's information criterion
BIC | 25841.603 Bayesian information criterion
---------------------+------------------------------------------------------
Baseline comparison |
CFI | 0.997 Comparative fit index
TLI | 0.992 Tucker-Lewis index
---------------------+------------------------------------------------------
Size of residuals |
SRMR | 0.014 Standardized root mean squared residual
CD | 0.087 Coefficient of determination
----------------------------------------------------------------------------
estat residuals
Residuals of observed variables
Mean residuals
| THYREOI~A BARN~1606 PP_ADHD~S logCd logCo logAs T~ish_I~e Materna~e
-------------+----------------------------------------------------------------------------------------
raw | 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
------------------------------------------------------------------------------------------------------
| Materna~u Parity MADHD_SS
-------------+---------------------------------
raw | 0.000 0.000 0.000
-----------------------------------------------
Covariance residuals
| THYREOI~A BARN~1606 PP_ADHD~S logCd logCo logAs T~ish_I~e Materna~e
-------------+----------------------------------------------------------------------------------------
THYREOIDEA | -0.000
BARN_DN~1606 | 0.000 0.000
PP_ADHD_SS | 0.015 -0.010 -0.017
logCd | 0.000 0.000 0.000 0.000
logCo | 0.000 0.000 0.000 0.000 0.000
logAs | -0.000 -0.000 0.000 0.000 0.000 0.000
TOTAL_Fish~e | 0.065 -0.111 -0.020 0.000 0.000 0.000 0.000
Maternal_age | 0.000 0.002 -0.000 0.000 0.000 0.000 0.000 0.000
Maternal_edu | -0.007 0.014 0.002 0.000 0.000 0.000 0.000 0.000
Parity | 0.002 0.015 -0.005 0.000 0.000 0.000 0.000 0.000
MADHD_SS | 0.018 0.008 -0.015 0.000 0.000 0.000 0.000 0.000
------------------------------------------------------------------------------------------------------
| Materna~u Parity MADHD_SS
-------------+---------------------------------
Maternal_edu | 0.000
Parity | 0.000 0.000
MADHD_SS | 0.000 0.000 0.000
-----------------------------------------------
Best regards,
Kjell
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