Simple Multilevel Model with PROC MIXED

[Cuneyt]

Dear All,

I am probably making a very simple and silly mistake in my code and I hope you guys can quickly point it out to me. I am estimating a very simple model as shown below. But the random variables are all come out as zero. Any help will be greatly appreciated.

Sincerely,

Cuneyt

data mydata;
	input y industry;
datalines;
-0.0005	326
-0.0092	326
 0.0107	321
-0.0463	321
 0.0088	321
-0.0051	335
 0.0000	335
-0.0009	327
-0.0031	327
-0.0055	336
 0.0157	336
 0.0095	336
-0.0132	336
 0.0196	336
 0.0187	336
-0.0071	336
-0.0154	321
 0.0155	321
-0.0155	321
 0.0145	321
;
run;

proc mixed data=mydata covtest;
	class industry;
	model y =  / solution ddfm=bw;
	random intercept / subject = industry solution;
run;

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr > Z
Intercept	industry	0	.	.	.
Residual		0.000248	0.000080	3.08	0.0010

Fit Statistics
-2 Res Log Likelihood	-100.8
AIC (Smaller is Better)	-98.8
AICC (Smaller is Better)	-98.6
BIC (Smaller is Better)	-99.2

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > |t|
Intercept	-0.00044	0.003519	4	-0.13	0.9065

Solution for Random Effects
Effect	industry	Estimate	Std Err Pred	DF	t Value	Pr > |t|
Intercept	321	0	.	.	.	.
Intercept	326	0	.	.	.	.
Intercept	327	0	.	.	.	.
Intercept	335	0	.	.	.	.
Intercept	336	0	.	.	.	.

[SteveDenham]

The most likely answer is that there is either insufficient variablility or insufficient sample size to estimate a variance component for industry.  So the answer to how to get a value using a REML method is to increase the sample size, if possible.  A non-maximum likelihood method might be to use PROC VARCOMP or PROC GLM to estimate the variance using a method of moments approach.

SteveDenham

[Cuneyt]

Hello Steve,

Thanks for your response. Even when I this same model with my original data set with 141,000 observations, I get an estimate of zero variance for the random effects. The SAS output is below. There are 96 subjects (naics4=industries). I seriously doubt that there is insufficient (virtually zero) variability within these subjects. What do you think?

The SAS System

The Mixed Procedure

Model Information
Data Set	IG.SURVEYS6
Dependent Variable	ch_tot_cases
Covariance Structure	Variance Components
Subject Effect	naics4
Estimation Method	ML
Residual Variance Method	Profile
Fixed Effects SE Method	Model-Based
Degrees of Freedom Method	Between-Within

Class Level Information
Class	Levels	Values
naics4	96	3111 3112 3113 3114 3115 3116 3117 3118 3119 3121 3122 3131 3132 3133 3141 3149 3151 3152 3159 3161 3162 3169 3211 3212 3216 3219 3221 3222 3223 3228 3231 3241 3251 3252 3253 3254 3255 3256 3259 3261 3262 3271 3272 3273 3274 3279 3311 3312 3313 3314 3315 3316 3320 3321 3322 3323 3324 3325 3326 3327 3328 3329 3331 3332 3333 3334 3335 3336 3339 3341 3342 3343 3344 3345 3346 3351 3352 3353 3359 3361 3362 3363 3364 3365 3366 3369 3371 3372 3379 3390 3391 3399 3441 3523 3541 3728

Dimensions
Covariance Parameters	2
Columns in X	1
Columns in Z per Subject	1
Subjects	96
Max Obs per Subject	9470

Number of Observations
Number of Observations Read	141041
Number of Observations Used	141008
Number of Observations Not Used	33

Iteration History
Iteration	Evaluations	-2 Log Like	Criterion
0	1	884853.71160320
1	1	884853.71160320	0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm	Subject	Estimate	Standard Error	Z Value	Pr > Z
Intercept	naics4	0	.	.	.
Residual		31.1036	0.1171	265.53	<.0001

Fit Statistics
-2 Log Likelihood	884853.7
AIC (Smaller is Better)	884857.7
AICC (Smaller is Better)	884857.7
BIC (Smaller is Better)	884862.8

Solution for Fixed Effects
Effect	Estimate	Standard Error	DF	t Value	Pr > |t|
Intercept	-0.01564	0.01485	95	-1.05	0.2950

Solution for Random Effects
Effect	naics4	Estimate	Std Err Pred	DF	t Value	Pr > |t|
Intercept	3111	0	.	.	.	.
Intercept	3112	0	.	.	.	.
Intercept	3113	0	.	.	.	.
Intercept	3114	0	.	.	.	.
Intercept	3115	0	.	.	.	.
Intercept	3116	0	.	.	.	.
Intercept	3117	0	.	.	.	.
Intercept	3118	0	.	.	.	.
Intercept	3119	0	.	.	.	.
Intercept	3121	0	.	.	.	.
Intercept	3122	0	.	.	.	.
Intercept	3131	0	.	.	.	.
Intercept	3132	0	.	.	.	.
Intercept	3133	0	.	.	.	.
Intercept	3141	0	.	.	.	.
Intercept	3149	0	.	.	.	.
Intercept	3151	0	.	.	.	.
Intercept	3152	0	.	.	.	.
Intercept	3159	0	.	.	.	.
Intercept	3161	0	.	.	.	.
Intercept	3162	0	.	.	.	.
Intercept	3169	0	.	.	.	.
Intercept	3211	0	.	.	.	.
Intercept	3212	0	.	.	.	.
Intercept	3216	0	.	.	.	.
Intercept	3219	0	.	.	.	.
Intercept	3221	0	.	.	.	.
Intercept	3222	0	.	.	.	.
Intercept	3223	0	.	.	.	.
Intercept	3228	0	.	.	.	.
Intercept	3231	0	.	.	.	.
Intercept	3241	0	.	.	.	.
Intercept	3251	0	.	.	.	.
Intercept	3252	0	.	.	.	.
Intercept	3253	0	.	.	.	.
Intercept	3254	0	.	.	.	.
Intercept	3255	0	.	.	.	.
Intercept	3256	0	.	.	.	.
Intercept	3259	0	.	.	.	.
Intercept	3261	0	.	.	.	.
Intercept	3262	0	.	.	.	.
Intercept	3271	0	.	.	.	.
Intercept	3272	0	.	.	.	.
Intercept	3273	0	.	.	.	.
Intercept	3274	0	.	.	.	.
Intercept	3279	0	.	.	.	.
Intercept	3311	0	.	.	.	.
Intercept	3312	0	.	.	.	.
Intercept	3313	0	.	.	.	.
Intercept	3314	0	.	.	.	.
Intercept	3315	0	.	.	.	.
Intercept	3316	0	.	.	.	.
Intercept	3320	0	.	.	.	.
Intercept	3321	0	.	.	.	.
Intercept	3322	0	.	.	.	.
Intercept	3323	0	.	.	.	.
Intercept	3324	0	.	.	.	.
Intercept	3325	0	.	.	.	.
Intercept	3326	0	.	.	.	.
Intercept	3327	0	.	.	.	.
Intercept	3328	0	.	.	.	.
Intercept	3329	0	.	.	.	.
Intercept	3331	0	.	.	.	.
Intercept	3332	0	.	.	.	.
Intercept	3333	0	.	.	.	.
Intercept	3334	0	.	.	.	.
Intercept	3335	0	.	.	.	.
Intercept	3336	0	.	.	.	.
Intercept	3339	0	.	.	.	.
Intercept	3341	0	.	.	.	.
Intercept	3342	0	.	.	.	.
Intercept	3343	0	.	.	.	.
Intercept	3344	0	.	.	.	.
Intercept	3345	0	.	.	.	.
Intercept	3346	0	.	.	.	.
Intercept	3351	0	.	.	.	.
Intercept	3352	0	.	.	.	.
Intercept	3353	0	.	.	.	.
Intercept	3359	0	.	.	.	.
Intercept	3361	0	.	.	.	.
Intercept	3362	0	.	.	.	.
Intercept	3363	0	.	.	.	.
Intercept	3364	0	.	.	.	.
Intercept	3365	0	.	.	.	.
Intercept	3366	0	.	.	.	.
Intercept	3369	0	.	.	.	.
Intercept	3371	0	.	.	.	.
Intercept	3372	0	.	.	.	.
Intercept	3379	0	.	.	.	.
Intercept	3390	0	.	.	.	.
Intercept	3391	0	.	.	.	.
Intercept	3399	0	.	.	.	.
Intercept	3441	0	.	.	.	.
Intercept	3523	0	.	.	.	.
Intercept	3541	0	.	.	.	.
Intercept	3728	0	.	.	.	.

[StatsMan]

MIXED puts a lower bound of 0 on variance components when ML or REML is used. If you switch to METHOD=TYPE3 in MIXED, that will remove the boundary and you should get a negative estimate for the variance on industry. 

What @SteveDenham says is correct. For this data, there is insufficient variability in the response to attribute variability to the industry effect. It may be that the variation within an industry is much greater than the variation between industries. 

If you treat industry as a fixed effect, my guess is that the effect of industry is highly insignificant. This is true for the sample of data provided. I understand that you do not want to use industry as fixed, but that may help explain that there is just not much difference across the industries compared to the differences seen within an industry.  

[Cuneyt]

This makes sense. Thank you very much.