## Example 56.3 Monotone Regression Method

This example uses the regression method to impute missing values for all variables in a data set with a monotone missing pattern. The following statements invoke the MI procedure and request the regression method for the variable Length2 and the predictive mean matching method for variable Length3. The resulting data set is named outex3.

```proc mi data=Fish1 round=.1  mu0= 0 35 45
seed=13951639 out=outex3;
monotone reg(Length2/ details)
regpmm(Length3= Length1 Length2 Length1*Length2/ details);
var Length1 Length2 Length3;
run;
```

The ROUND= option is used to round the imputed values to the same precision as observed values. The values specified with the ROUND= option are matched with the variables Length1, Length2, and Length3 in the order listed in the VAR statement. The MU0= option requests t tests for the hypotheses that the population means corresponding to the variables in the VAR statement are Length2=35 and Length3=45.

The "Missing Data Patterns" table lists distinct missing data patterns with corresponding frequencies and percentages. It is identical to the table in Output 56.2.3 in Example 56.2.

The "Monotone Model Specification" table in Output 56.3.1 displays the model specification.

Output 56.3.1 Monotone Model Specification
The MI Procedure

Monotone Model Specification
Method Imputed Variables
Regression Length2
Regression-PMM( K= 5) Length3

When you use the DETAILS option, the parameters estimated from the observed data and the parameters used in each imputation are displayed in Output 56.3.2 and Output 56.3.3.

Output 56.3.2 Regression Model
Regression Models for Monotone Method
Imputed
Variable
Effect Obs-Data Imputation
1 2 3 4 5
Length2 Intercept -0.04249 -0.049184 -0.055470 -0.051346 -0.064193 -0.030719
Length2 Length1 0.98587 1.001934 0.995275 0.992294 0.983122 0.995883

Output 56.3.3 Regression Predicted Mean Matching Model
Regression Models for Monotone Predicted Mean Matching Method
Imputed
Variable
Effect Obs Data Imputation
1 2 3 4 5
Length3 Intercept -0.01304 0.004134 -0.011417 -0.034177 -0.010532 0.004685
Length3 Length1 -0.01332 0.025320 -0.037494 0.308765 0.156606 -0.147118
Length3 Length2 0.98918 0.955510 1.025741 0.673374 0.828384 1.146440
Length3 Length1*Length2 -0.02521 -0.034964 -0.022017 -0.017919 -0.029335 -0.034671

After the completion of five imputations by default, the "Variance Information" table in Output 56.3.4 displays the between-imputation variance, within-imputation variance, and total variance for combining complete-data inferences. The relative increase in variance due to missingness, the fraction of missing information, and the relative efficiency for each variable are also displayed. These statistics are described in the section Combining Inferences from Multiply Imputed Data Sets.

Output 56.3.4 Variance Information
Variance Information
Variable Variance DF Relative
Increase
in Variance
Fraction
Missing
Information
Relative
Efficiency
Between Within Total
Length2 0.000133 0.439512 0.439672 32.15 0.000363 0.000363 0.999927
Length3 0.000386 0.486913 0.487376 32.131 0.000952 0.000951 0.999810

The "Parameter Estimates" table in Output 56.3.5 displays a 95% mean confidence interval and a t statistic with its associated p-value for each of the hypotheses requested with the MU0= option.

Output 56.3.5 Parameter Estimates
Parameter Estimates
Variable Mean Std Error 95% Confidence Limits DF Minimum Maximum Mu0 t for H0:
Mean=Mu0
Pr > |t|
Length2 33.104571 0.663078 31.75417 34.45497 32.15 33.088571 33.117143 35.000000 -2.86 0.0074
Length3 38.424571 0.698123 37.00277 39.84637 32.131 38.397143 38.445714 45.000000 -9.42 <.0001

The following statements list the first 10 observations of the data set outex3 in Output 56.3.6. Note that the imputed values of Length2 are rounded to the same precision as the observed values.

```proc print data=outex3(obs=10);
title 'First 10 Observations of the Imputed Data Set';
run;
```

Output 56.3.6 Imputed Data Set
 First 10 Observations of the Imputed Data Set

Obs _Imputation_ Length1 Length2 Length3
1 1 23.2 25.4 30.0
2 1 24.0 26.3 31.2
3 1 23.9 26.5 31.1
4 1 26.3 29.0 33.5
5 1 26.5 29.0 34.7
6 1 26.8 29.7 34.7
7 1 26.8 28.8 34.7
8 1 27.6 30.0 35.0
9 1 27.6 30.0 35.1
10 1 28.5 30.7 36.2