In PROC QLIM, missing or zero standard errors and missing t  and p -values commonly occur when the Hessian matrix is singular or nearly singular. This can happen for many different reasons depending on the data and/or model. One very common situation that can result in the Hessian being singular or nearly singular is poorly scaled variables. In the following example, a poorly scaled variable in the model results in zero standard errors and missing t  and p -values. You can avoid the problem by rescaling the variable.

The following statements create the data set to be modeled. In these data, Hours is the number of hours the wife worked outside the household in a given year, Yrs_Ed is the years of education, and Yrs_Exp is the years of work experience. The variable, Hrs_Exp, is created giving work experience measured in minutes.

      data test;
         input Hours Yrs_Ed Yrs_Exp;
         Min_Exp = Yrs_Exp*365*24*60;
         datalines;
         0 8 9
         0 8 12
         0 9 10
         0 10 15
         0 11 4
         0 11 6
         1000 12 1
         1960 12 29
         0 13 3 
         2100 13 36
         3686 14 11
         1920 14 38
         0 15 14
         1728 16 3
         1568 16 19
         1316 17 7
         0 17 15
         ; 

Notice that when measured on the minute scale, the values of work experience are quite large.

      proc print data=test noobs; 
         var Hours Yrs_Ed Min_Exp;
         run; 

Hours	Yrs_Ed	Min_Exp
0	8	4730400
0	8	6307200
0	9	5256000
0	10	7884000
0	11	2102400
0	11	3153600
1000	12	525600
1960	12	15242400
0	13	1576800
2100	13	18921600
3686	14	5781600
1920	14	19972800
0	15	7358400
1728	16	1576800
1568	16	9986400
1316	17	3679200
0	17	7884000

 

Fitting a tobit model to the above data results in zero standard error for the Min_Exp parameter. The corresponding t  value and p -value are missing.

      proc qlim data=test;
         model Hours = Yrs_Ed Min_Exp;
         endogenous Hours ~ censored(lb=0);
      run; 

Parameter Estimates
Parameter	DF	Estimate	Standard Error	t Value	Approx
					Pr > |t|
Intercept	1	-5598.64	28.27529	-198	<.0001
Yrs_Ed	1	373.1477	54.38262	6.86	<.0001
Min_Exp	1	0.000121	0	.	.
_Sigma	1	1582.87	391.186	4.05	<.0001

 

The problem is caused by the extremely large values of the work experience predictor when measured in minutes. You can avoid the problem by rescaling this predictor to have smaller values. By using work experience measured in years (Yrs_Exp) rather than in minutes (Min_Exp), the information is retained but the values are much smaller.

      proc print data=test noobs; 
         var Hours Yrs_Ed Yrs_Exp;
         run;

Hours	Yrs_Ed	Yrs_Exp
0	8	9
0	8	12
0	9	10
0	10	15
0	11	4
0	11	6
1000	12	1
1960	12	29
0	13	3
2100	13	36
3686	14	11
1920	14	38
0	15	14
1728	16	3
1568	16	19
1316	17	7
0	17	15

 

Refitting the model using the rescaled predictor produces a reasonable standard error estimate as well as t  and p -values.

      proc qlim data=test;
         model Hours = Yrs_Ed Yrs_Exp;
         endogenous Hours ~ censored(lb=0);
      run;

Parameter Estimates
Parameter	DF	Estimate	Standard Error	t Value	Approx
					Pr > |t|
Intercept	1	-5598.3	27.69222	-202.16	<.0001
Yrs_Ed	1	373.1233	53.98888	6.91	<.0001
Yrs_Exp	1	63.33625	36.5513	1.73	0.0831
_Sigma	1	1582.86	390.0765	4.06	<.0001