Random effects prediction and interpretation in multilevel logit models

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rahulvbb
Posts: 9
Joined: Thu Feb 19, 2015 1:01 pm

Random effects prediction and interpretation in multilevel logit models

Post by rahulvbb »

Dear All,

I have estimated 3 level random intercept logit model. Also, I have predicted the random effects and its std.error.
The codes used are as follows.

Code: Select all

#delimit ; 
runmlwin d2  cons t2-t10  i.b4_1 i.b4_2  mort1 mort2 i.ageR2  i.yrsch i.wealthq i.work i.v025 i.caste i.religion diff 
 female_lit density urban sexratio poverty imr female_work nsdp  med_age_marr,
level3(state:cons,residuals(v))level2(stateyear1:cons, residuals(u))level1(episodeid:)
discrete(distribution(binomial) link(logit) denominator(cons) pql2) 
mlwinsettings(size(536000) levels(5) columns(1500) variables(300) optimat) nopaus;
#delimit cr
Now, I want to know if the procedure is correct. How to interpret the estimates of random effects? And what if the these effects are not significant.
The results are given below.

Thank you.

-----------------------------------------------------------
| No. of Observations per Group
Level Variable | Groups Minimum Average Maximum
----------------+------------------------------------------
state | 25 5191 19054.8 59357
stateyear1 | 900 17 529.3 2992
-----------------------------------------------------------

Run time (seconds) = 796.44
Number of iterations = 12
------------------------------------------------------------------------------
d2 | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cons | .1090683 .9636476 0.11 0.910 -1.779646 1.997783
t2 | 1.931034 .0107587 179.49 0.000 1.909947 1.952121
t3 | 2.081403 .0121121 171.85 0.000 2.057663 2.105142
t4 | 1.751582 .014734 118.88 0.000 1.722704 1.78046
t5 | 1.456051 .0182646 79.72 0.000 1.420253 1.491849
t6 | 1.097937 .0233003 47.12 0.000 1.052269 1.143605
t7 | .7370105 .0299055 24.64 0.000 .6783968 .7956243
t8 | .4126172 .0377839 10.92 0.000 .338562 .4866724
t9 | .010698 .0494809 0.22 0.829 -.0862828 .1076787
t10 | .7283634 .0414813 17.56 0.000 .6470615 .8096653
_1b_b4_1 | 0 0 . . 0 0
_2_b4_1 | .1017074 .0073527 13.83 0.000 .0872964 .1161183
_1b_b4_2 | 0 0 . . 0 0
_2_b4_2 | .1573613 .0073399 21.44 0.000 .1429753 .1717472
mort1 | .0175835 .0112936 1.56 0.119 -.0045514 .0397185
mort2 | .2186041 .0141917 15.40 0.000 .1907888 .2464194
_1b_ageR2 | 0 0 . . 0 0
_2_ageR2 | -.1019088 .0087927 -11.59 0.000 -.1191423 -.0846754
_3_ageR2 | -.3416576 .0129397 -26.40 0.000 -.3670189 -.3162963
_4_ageR2 | -.6870595 .0272384 -25.22 0.000 -.7404458 -.6336732
_5_ageR2 | -1.03705 .0786868 -13.18 0.000 -1.191273 -.8828265
_0b_yrsch | 0 0 . . 0 0
_1_yrsch | -.0501475 .0110335 -4.55 0.000 -.0717727 -.0285223
_2_yrsch | -.2356844 .0123127 -19.14 0.000 -.2598167 -.211552
_3_yrsch | -.8280034 .0152081 -54.45 0.000 -.8578107 -.7981961
_1b_wealthq | 0 0 . . 0 0
_2_wealthq | .0584479 .0127415 4.59 0.000 .0334749 .0834209
_3_wealthq | .1113001 .0128843 8.64 0.000 .0860474 .1365527
_4_wealthq | .082883 .0138856 5.97 0.000 .0556676 .1100983
_5_wealthq | -.1020844 .0168653 -6.05 0.000 -.1351397 -.069029
_0b_work | 0 0 . . 0 0
_1_work | -.0093469 .0092149 -1.01 0.310 -.0274077 .0087139
_1b_v025 | 0 0 . . 0 0
_2_v025 | .0420282 .0102944 4.08 0.000 .0218516 .0622048
_1b_caste | 0 0 . . 0 0
_2_caste | -.0424186 .0159984 -2.65 0.008 -.0737749 -.0110623
_3_caste | -.140725 .0106329 -13.23 0.000 -.1615652 -.1198849
_1b_religion | 0 0 . . 0 0
_2_religion | .2270972 .0120155 18.90 0.000 .2035473 .2506471
_3_religion | -.0016808 .0157864 -0.11 0.915 -.0326217 .02926
diff | -.0130624 .0002427 -53.82 0.000 -.0135381 -.0125867
female_lit | -.0139716 .002543 -5.49 0.000 -.0189559 -.0089874
density | .0000225 .0000216 1.04 0.299 -.0000199 .0000649
urban | .0137419 .0029296 4.69 0.000 .0080001 .0194838
sexratio | -.0009488 .000866 -1.10 0.273 -.0026462 .0007486
poverty | .0015769 .0019049 0.83 0.408 -.0021566 .0053104
imr | -.0008813 .0008145 -1.08 0.279 -.0024777 .0007152
female_work | -.0024098 .0021077 -1.14 0.253 -.0065409 .0017213
nsdp | -.0000258 2.47e-06 -10.43 0.000 -.0000306 -.0000209
med_age_marr | -.0231153 .0261615 -0.88 0.377 -.0743909 .0281604
------------------------------------------------------------------------------

------------------------------------------------------------------------------
Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval]
-----------------------------+------------------------------------------------
Level 3: state |
var(cons) | .0809512 .023465 .0349607 .1269417
-----------------------------+------------------------------------------------
Level 2: stateyear1 |
var(cons) | .0520777 .003336 .0455392 .0586163
------------------------------------------------------------------------------




Summary statistics: mean
by categories of: state (RECODE of v024 (state))

state | v0 v0se
-----------------+--------------------
Jammu and Kashmi | -.3359869 .1059516
Himachal Pradesh | .3888001 .0989626
Punjab | .0884756 .1046537
Haryana | .0597908 .1045056
Delhi | -.4607291 .2160253
Rajasthan | -.2377929 .0832677
Uttar pradesh | -.2503015 .0909252
Bihar | -.3126784 .0787578
Arunanchal Prade | -.0454318 .114413
Nagaland | .4550074 .1044245
Manipur | .1553641 .0963122
Mizoram | .7130891 .1104397
Tripura | -.2760562 .0867473
Meghalaya | .2167409 .0934108
Assam | -.1248221 .0863468
West bengal | -.4308518 .0826869
Orrisa | -.1824791 .0916045
Madhya Pradesh | -.0825534 .0819738
Gujrat | .124661 .0787473
Maharashtra | .1662242 .0862267
Andhra Pradesh | -.0408329 .1008229
Karnataka | .0449862 .0796471
Goa | .1684438 .094427
Kerala | .2842513 .1262546
Tamil Nadu | -.0858196 .0957084
-----------------+--------------------
Total | -.0774662 .0966015
--------------------------------------
GeorgeLeckie
Site Admin
Posts: 432
Joined: Fri Apr 01, 2011 2:14 pm

Re: Random effects prediction and interpretation in multilevel logit models

Post by GeorgeLeckie »

Dear rahulvbb,

The predicted state random effects measure how much higher the predicted log-odds are in each state relative to the average state.

Researchers often plot these in a caterpillar plot to aide graphical interpretation. You can do this using the -serrbar- command.

Best wishes

George
rahulvbb
Posts: 9
Joined: Thu Feb 19, 2015 1:01 pm

Re: Random effects prediction and interpretation in multilevel logit models

Post by rahulvbb »

Dear sir,
Thank you for your response. Its very helpful. I have one more question: the significance of these predicted values based on estimated std errors!!!!!
Do we need to check the statistical significance of these effects?
In my case none of the effect is statistically significant.
Please suggest.
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