Hi all,
I'm looking use a linear mixed model to analyze longitudinal changes in parental anxiety during the course of their child's oral immunotherapy. At it's most simple, the model has 3 variables. My DV total_impact measures parental anxiety continuously. I also have a discrete time variable (4 time points): con_time and a subject variable called id.
When I run the model with just random intercepts the output looks unremarkable: anxiety goes down over time and the baseline level of anxiety varies to some degree. However, if I include a random slope component to the model, the results look a little more bizarre, particularly when I specificy an unstructured covariance stucture. In particular, the standard errors on some of the random effects seem unusually large. See below
When I use the default covariance structure, however, the standard errors appear to be so small as to not be visible in the output.
I'm new to linear mixed models, so I would be very grateful if anyone can offer some insight into why the standard errors are so large in one model and very small in the other.
thanks,
-Mike
I'm looking use a linear mixed model to analyze longitudinal changes in parental anxiety during the course of their child's oral immunotherapy. At it's most simple, the model has 3 variables. My DV total_impact measures parental anxiety continuously. I also have a discrete time variable (4 time points): con_time and a subject variable called id.
When I run the model with just random intercepts the output looks unremarkable: anxiety goes down over time and the baseline level of anxiety varies to some degree. However, if I include a random slope component to the model, the results look a little more bizarre, particularly when I specificy an unstructured covariance stucture. In particular, the standard errors on some of the random effects seem unusually large. See below
Code:
xtmixed total_impact i.con_time, reml||id:i.con_time, cov(un) Performing EM optimization: Performing gradient-based optimization: Iteration 0: Log restricted-likelihood = -2246.5011 (not concave) Iteration 1: Log restricted-likelihood = -2243.7042 (not concave) Iteration 2: Log restricted-likelihood = -2243.1187 Iteration 3: Log restricted-likelihood = -2242.8357 Iteration 4: Log restricted-likelihood = -2242.7075 Iteration 5: Log restricted-likelihood = -2242.7061 Iteration 6: Log restricted-likelihood = -2242.7061 Computing standard errors: Mixed-effects REML regression Number of obs = 505 Group variable: id Number of groups = 333 Obs per group: min = 1 avg = 1.5 max = 4 Wald chi2(3) = 100.57 Log restricted-likelihood = -2242.7061 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ total_impact | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- con_time | 2 | -16.48735 1.903727 -8.66 0.000 -20.21859 -12.75611 3 | -20.92988 2.450287 -8.54 0.000 -25.73235 -16.1274 4 | -20.9626 2.711521 -7.73 0.000 -26.27708 -15.64812 | _cons | 73.2775 1.882855 38.92 0.000 69.58717 76.96783 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects parameters | Estimate Std. err. [95% conf. interval] -----------------------------+------------------------------------------------ id: Unstructured | sd(2.con_time) | 19.91303 111.885 .0003285 1207166 sd(3.con_time) | 25.14283 88.64329 .0250857 25200.06 sd(4.con_time) | 24.53929 90.87722 .0172814 34845.47 sd(_cons) | 25.88462 43.05445 .9936193 674.3164 corr(2.con_time,3.con_time) | .9040906 3.81578 -1 1 corr(2.con_time,4.con_time) | .7601554 2.526025 -1 1 corr(2.con_time,_cons) | -.6110516 .1409119 -.8182008 -.2634813 corr(3.con_time,4.con_time) | .650417 1.095818 -.9944983 .9997525 corr(3.con_time,_cons) | -.7728544 .5873255 -.9991575 .9499431 corr(4.con_time,_cons) | -.7283099 .4030614 -.9891898 .6394607 -----------------------------+------------------------------------------------ sd(Residual) | 6.716628 165.8342 6.47e-21 6.97e+21 ------------------------------------------------------------------------------ LR test vs. linear model: chi2(10) = 92.75 Prob > chi2 = 0.0000
Code:
xtmixed total_impact i.con_time, reml||id:i.con_time Performing EM optimization: Performing gradient-based optimization: Iteration 0: Log restricted-likelihood = -2307.5562 (not concave) Iteration 1: Log restricted-likelihood = -2271.955 Iteration 2: Log restricted-likelihood = -2262.1338 Iteration 3: Log restricted-likelihood = -2260.2227 Iteration 4: Log restricted-likelihood = -2260.1745 Iteration 5: Log restricted-likelihood = -2260.1743 Computing standard errors: Mixed-effects REML regression Number of obs = 505 Group variable: id Number of groups = 333 Obs per group: min = 1 avg = 1.5 max = 4 Wald chi2(3) = 123.22 Log restricted-likelihood = -2260.1743 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ total_impact | Coefficient Std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- con_time | 2 | -17.17941 1.897695 -9.05 0.000 -20.89883 -13.46 3 | -20.02102 2.57513 -7.77 0.000 -25.06819 -14.97386 4 | -20.6856 2.704244 -7.65 0.000 -25.98582 -15.38538 | _cons | 73.51702 1.617422 45.45 0.000 70.34693 76.68711 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects parameters | Estimate Std. err. [95% conf. interval] -----------------------------+------------------------------------------------ id: Independent | sd(2.con_time) | .0000629 . . . sd(3.con_time) | .0000223 . . . sd(4.con_time) | .0002007 . . . sd(_cons) | 17.0865 . . . -----------------------------+------------------------------------------------ sd(Residual) | 15.52083 . . . ------------------------------------------------------------------------------ LR test vs. linear model: chi2(4) = 57.81 Prob > chi2 = 0.0000
thanks,
-Mike
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