I'm wondering about the best way to do multiple imputation (mi impute chained) with panel data. My goal is to compute a mixed effects model looking at the effect of an intervention on mental health over time, with interaction effects to test how the intervention differs by subgroup. Right now, I have two concerns: (1) my final model (below) won't compute the standard error of the random slope, and (2) I'm worried my imputation method is biasing the Time2 value to zero.
Here is my approach to multiple imputation:
My final model (in bold) isn't computing the standard error for the random slope, which makes me worry I've done something wrong.
Below, I show the unconditional growth models, and then the full model.
Here is my approach to multiple imputation:
Code:
keep record_id week pos_asp_total memtot care_80plus delay age sex college income_binary white cbi_Dev pmhT ppaT
mi set mlong
mi xtset, clear
mi misstable sum pos_asp_total memtot care_80plus delay age sex college income_binary white cbi_Dev pmhT ppaT
// cbi_Dev pmhT ppaT = highly correlated with pos_asp
mi reshape wide pos_asp_total cbi_Dev pmhT ppaT , i(record_id) j(week) // only for time-variant vars
drop pmhT4 pmhT8 pmhT12 pmhT20 // we only have observations at T0 and T16
mi register imputed pos_asp_total* memtot* care_80plus delay age sex college income_binary white cbi_Dev* pmhT* ppaT*
mi impute chained (regress) pos_asp_total* memtot* age cbi_Dev* pmhT* ppaT* ///
(logit, augment) care_80plus delay sex college income_binary white, ///
add(50) rseed(12345) chaindots
mi reshape long pos_asp_total cbi_Dev pmhT ppaT, i(record_id) j(week)
gen qweek = week*week
mi xtset record_id week
mi estimate: mixed pos_asp_total week qweek ||record_id: week , vce(robust)
// results show qweek isn't significant at p <.05
// full model using week but not qweek:
mi estimate: mixed pos_asp_total (c.week)##(c.memtot c.care_80plus c.delay c.age ///
c.sex c.college c.income_binary c.white) || record_id: week , vce(robust)
My final model (in bold) isn't computing the standard error for the random slope, which makes me worry I've done something wrong.
Below, I show the unconditional growth models, and then the full model.
Code:
mi estimate: mixed pos_asp_total week qweek ||record_id: week , vce(robust) Multiple-imputation estimates Imputations = 50 Mixed-effects regression Number of obs = 1,002 Group variable: record_id Number of groups = 167 Obs per group: min = 6 avg = 6.0 max = 6 Average RVI = 0.2134 Largest FMI = 0.2587 DF adjustment: Large sample DF: min = 743.50 avg = 5,263.93 max = 22,119.19 Model F test: Equal FMI F( 2, 3075.0) = 15.31 Within VCE type: Robust Prob > F = 0.0000 (Within VCE adjusted for 167 clusters in record_id) ------------------------------------------------------------------------------- pos_asp_total | Coefficient Std. err. t P>|t| [95% conf. interval] --------------+---------------------------------------------------------------- week | .3013896 .0909797 3.31 0.001 .1229984 .4797808 qweek | -.0075897 .0042899 -1.77 0.077 -.016002 .0008226 _cons | 25.96917 .7484187 34.70 0.000 24.50221 27.43612 ------------------------------------------------------------------------------- ------------------------------------------------------------------------------ Random-effects parameters | Estimate Std. err. [95% conf. interval] -----------------------------+------------------------------------------------ record_id: Independent | sd(week) | .1393417 .0732631 .0496371 .3911613 sd(_cons) | 7.830683 .4448212 7.005151 8.7535 -----------------------------+------------------------------------------------ sd(Residual) | 4.841603 .2246497 4.420391 5.302952 ------------------------------------------------------------------------------ *** Since qweek (aka Time2) is only marginally significant, I try using only week (linear time). . mi estimate: mixed pos_asp_total week ||record_id: week , vce(robust) Multiple-imputation estimates Imputations = 50 Mixed-effects regression Number of obs = 1,002 Group variable: record_id Number of groups = 167 Obs per group: min = 6 avg = 6.0 max = 6 Average RVI = 0.2112 Largest FMI = 0.2368 DF adjustment: Large sample DF: min = 886.40 avg = 3,194.79 max = 10,400.25 Model F test: Equal FMI F( 1, 1287.8) = 27.83 Within VCE type: Robust Prob > F = 0.0000 (Within VCE adjusted for 167 clusters in record_id) ------------------------------------------------------------------------------- pos_asp_total | Coefficient Std. err. t P>|t| [95% conf. interval] --------------+---------------------------------------------------------------- week | .1495953 .0283557 5.28 0.000 .0939668 .2052238 _cons | 26.37395 .6970041 37.84 0.000 25.00769 27.74021 ------------------------------------------------------------------------------- ------------------------------------------------------------------------------ Random-effects parameters | Estimate Std. err. [95% conf. interval] -----------------------------+------------------------------------------------ record_id: Independent | sd(week) | .1375319 .0792575 .0443811 .4261951 sd(_cons) | 7.830294 .4451679 7.004154 8.753877 -----------------------------+------------------------------------------------ sd(Residual) | 4.855943 .2229362 4.437741 5.313555 ------------------------------------------------------------------------------ *** I then try my full model, which looks at how the linear growth differs by age, sex, etc. Notice the weird missing information (e.g., standard error of the random slope) in red. . mi estimate: mixed pos_asp_total (c.week)##(c.memtot c.care_80plus c.delay c.age c.sex c.college c.income_binary c.whit > e) ||record_id: week , vce(robust) Multiple-imputation estimates Imputations = 50 Mixed-effects regression Number of obs = 1,002 Group variable: record_id Number of groups = 167 Obs per group: min = 6 avg = 6.0 max = 6 Average RVI = . Largest FMI = . DF adjustment: Large sample DF: min = 261.67 avg = . max = . Model F test: Equal FMI F( 17,10006.2) = 4.33 Within VCE type: Robust Prob > F = 0.0000 (Within VCE adjusted for 167 clusters in record_id) ---------------------------------------------------------------------------------------- pos_asp_total | Coefficient Std. err. t P>|t| [95% conf. interval] -----------------------+---------------------------------------------------------------- week | .1896886 .2223539 0.85 0.394 -.2480316 .6274089 memtot | -.0148546 .0331565 -0.45 0.654 -.0798767 .0501674 care_80plus | -.800912 1.965325 -0.41 0.684 -4.654188 3.052364 delay | -1.392745 1.342752 -1.04 0.300 -4.024856 1.239367 age | .0448753 .0604383 0.74 0.458 -.0737715 .1635221 sex | -4.149532 1.698719 -2.44 0.015 -7.47977 -.8192944 college | -.598259 1.409668 -0.42 0.671 -3.361389 2.164871 income_binary | -1.384134 1.463121 -0.95 0.344 -4.252764 1.484495 white | -3.688123 1.947044 -1.89 0.058 -7.505826 .1295793 | c.week#c.memtot | .0013911 .0014019 0.99 0.321 -.0013595 .0041417 | c.week#c.care_80plus | .0860559 .0764048 1.13 0.261 -.0643748 .2364867 | c.week#c.delay | .0799039 .0581131 1.37 0.170 -.0343161 .1941239 | c.week#c.age | -.0046516 .0023817 -1.95 0.052 -.0093397 .0000365 | c.week#c.sex | .1674653 .0743649 2.25 0.025 .0210354 .3138951 | c.week#c.college | .1086531 .0570293 1.91 0.057 -.0032943 .2206005 | c.week#c.income_binary | -.0874567 .0709249 -1.23 0.219 -.2270465 .052133 | c.week#c.white | -.069466 .0901648 -0.77 0.441 -.2464458 .1075138 | _cons | 33.54938 5.188557 6.47 0.000 23.36598 43.73277 ---------------------------------------------------------------------------------------- ------------------------------------------------------------------------------ Random-effects parameters | Estimate Std. err. [95% conf. interval] -----------------------------+------------------------------------------------ record_id: Independent | sd(week) | .0212806 . . . sd(_cons) | 7.567774 .4906963 6.664248 8.593798 -----------------------------+------------------------------------------------ sd(Residual) | 4.82774 .2709785 4.324656 5.389347 ------------------------------------------------------------------------------
