Discussion Of Results

Presentation and Discussion of the Results

A. Descriptive Statistics of the actual data Descriptive Statistics Mean

Std.Dev

Minimum

Maximum

N

TOTEX2

102389.8 129866.6

8926.000

3203978

4130

TOTIN2

134119.4 216934.9

9067.000

4357180

4130

The above figure shows the descriptive statistics of the second visit actual data. The mean and the standard deviation of the data for TOTIN2 are larger than TOTEX2 primarily because most of the values from TOTIN2 are larger and vary significantly than TOTEX2. The statistics above will be used later in computing for the accurateness and precision of the imputed data. B. Formation of Imputation Classes Chi – Square Test for Independence Matching Variables PROV CODES1 CODEP1 Matching Variables PROV CODES1 CODEP1

TOTIN2 Test Stat P-Value 151.78 < 0.0001 613.859 < 0.0001 358.436 < 0.0001 Test Stat 137.83 687.342 193.132

TOTEX2 P-Value < 0.0001 < 0.0001 < 0.0001

Degrees of Freedom 9 6 9 Degrees of Freedom 9 6 9

A test of association using chi-square test for independence showed that all the candidates for the matching variable have a very significant relationship with both the nonresponse variables. In both nonresponse variables, CODES1 has the largest test statistics among all the candidates for the matching variable.

Measures of Association

MEASURES OF ASSOCIATION: INCOME VARIABLE PROVINCE CODES1 Phi-Coefficient 0.192 0.386 Cramer's V 0.111 0.273 Contingency Test 0.188 0.36 MEASURES OF ASSOCIATION: EXPENDITURE VARIABLE PROVINCE CODES1 Phi-Coefficient 0.183 0.408 Cramer's V 0.105 0.288 Contingency Test 0.18 0.378

CODEP1 0.295 0.17 0.283 CODEP1 0.216 0.125 0.211

In the results above, CODES1 has the highest association in all the tests to both nonresponse variables. In addition, it registered at least twenty percent, the minimum requirement mentioned in the methodology for it to be considered as a matching variable in all the tests. PROV fares the worst in the test for association after measuring below twenty percent in both nonresponse variable and tests for association. After dominating the tests for association, CODES1 has been chosen as matching variable for this study.

C. Distribution of the simulated data set by education status imputation classes for each nonresponse variable and nonresponse rates

CLASSES 1 2 3 TOTAL

TOTEX2, 10% NONRESPONSE RATE Total Number of Observations Observations set to Observations Retained Nonresponse Mean Mean No. % No. No. Rate Rate 2635 63.8% 2379 75602.76 256 78454.08 1434 34.7% 1280 137760.6 154 132438.5 61 1.5% 58 443518.3 3 157801.3 4130 100% 3717 102748.6 413 99160.23

Percentage of deleted Cases 9.7% 10.7% 4.9% 10.0%

The table above shows that mean of the respondents doesn’t significantly differ than the mean of the nonrespondents. However, in the third imputation class, the mean vary significantly between the respondent and nonrespondents. There were only three observations that were simulated to nonresponse as compared to almost ten and eleven percent from the first and second class respectively.

TOTEX2, 20% NONRESPONSE RATE

CLASSES 1 2 3 TOTAL

Total Number of Observations No.

%

2635 1434 61 4130

63.8% 34.7% 1.5% 100%

Observations Retained Mean No. Rate 2100 75446.62 1154 137492.3 50 412604.6 3304 102219.8

Observations set to Nonresponse Mean No. Rate 535 77580.03 280 135939.4 11 506112.1 826 103069.7

Percentage of nonresponse cases 20.3% 19.5% 18.0% 20.0%

Unlike the previous table with a half lower nonresponse rate, the table above showed the opposite. The mean of the nonrespondents vary significantly against the respondents. Also, the mean from the third class of the nonrespondents vary significantly from the respondents. The percentage of nonrespondents is almost equally distributed to each imputation class.

CLASSES 1 2 3 TOTAL

TOTEX2, 30% NONRESPONSE RATE Total Number of Observations Observations set to Observations Retained Nonresponse Mean Mean No. % No. No. Rate Rate 2635 63.8% 1833 75121.42 802 77613.02 1434 34.7% 1014 136477.1 420 138907.9 61 1.5% 44 342434.8 17 654725.5 4130 100% 2891 100709.9 1239 106309.4

Percentage of nonresponse cases 30.4% 29.3% 27.9% 30.0%

Results above showed didn’t differ significantly from the previous except that the mean from the each imputation classes are greater for the nonrespondents than the respondents especially from the third imputation class in which the mean of the respondents is almost just the half of the nonrespondents. Again, similar to the twenty percent nonresponse rate for TOTEX2, the distribution of nonrespondents for each class is almost equally distributed.

CLASSES

TOTIN2 , 10% NONRESPONSE RATE Total Number of Observations Observations set to Observations Retained Nonresponse Mean Mean No. % No. No. Rate Rate

Percentage of nonresponse cases

1 2 3 TOTAL

2635 1434 61 4130

63.8% 34.7% 1.5% 100%

2379 1280 58 3717

93569.17 187654.9 660909.9 134821.7

256 154 3 413

93766.26 181006.4 300630.7 127799.1

9.7% 10.7% 4.9% 10.0%

Like for the TOTEX2 variable from the lowest nonresponse rate, the percentage of nonrespondents for the TOTIN2 variable is the same. Unlike for TOTEX2, the mean of the respondents in all the classes significantly differ from the nonrespondents especially in the third imputation class where the nonrespondents mean is less than half of the respondents mean.

CLASSES 1 2 3 TOTAL

TOTIN2, 20% NONRESPONSE RATE Total Number of Observations Observations set to Observations Retained Nonresponse Mean Mean No. % No. No. Rate Rate 2635 63.8% 2100 93565.90 535 93676.31 1434 34.7% 1154 184817.6 280 195691.9 61 1.5% 50 634562.8 11 682411.3 4130 100% 3304 133624.7 826 136098.2

Percentage of nonresponse cases 20.3% 19.5% 18.0% 20.0%

Contrary to the lower nonresponse rate of TOTIN2, the mean coming from the nonrespondents in all imputation classes of the nonrespondents differ than the respondents. However, unlike from the previous results in both TOTIN2 and TOTEX2, the deviation of the nonrespondents and respondents from the second imputation class is surprisingly larger than the third imputation class.

CLASSES 1 2 3 TOTAL

TOTIN2, 30% NONRESPONSE RATE Total Number of Observations Observations set to Observations Retained Nonresponse Mean Mean No. % No. No. Rate Rate 2635 63.8% 1833 92972.55 802 94995.68 1434 34.7% 1014 181821.5 420 199300.6 61 1.5% 44 523326.6 17 953429.2 4130 100% 2891 130685.6 1239 142131.6

Percentage of nonresponse cases 30.4% 29.3% 27.9% 30.0%

The mean deviation of the nonrespondents and the nonrespondents for the results above has largest deviation from all the results coming from both nonresponse variables. Both the second and third imputation class has huge mean deviations. The mean rate of nonrespondents and respondents from the third imputation class has the largest and smallest value from all the nonresponse rates in the TOTIN2 respectively. D. Model Validation Results for Regression Imputation The following results for this section are the tests in validating the assumptions of a single regression model. For each imputation class, nonresponse variable and rate, different models were made and tested.

TOTEX, 10% Nonresponse Rate, First Imputation Class Summary Statistics MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

0.853 0.728 0.728 6363.590 0.000 0.277

Analysis of Variance (ANOVA) Sums of Squares

Df

Regression 486.5398 1

Mean Squares

p-level

486.5398 6363.590 0.00

Residual 181.7378 2377 0.0765 Total

F

668.2776 Durbin-Watson Test DW STAT

Serial

Estimate 2.075187 -0.038196

Normal Probability Plot

Expected Normal Value

Normal Probability Plot of Residuals 10 8 6 4 2 0 -2 -4 -6 -2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

12.0

12.5

2.0

2.5

13.0

13.5

Residuals

Predicted vs. Residuals Predicted vs. Residual Scores

Residuals

Dependent variable: LNSV 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 9.0

9.5

10.0

10.5

11.0 Predicted Values

11.5

95% confidence

Summary statistics for the first imputation class of the expenditure variable under ten percent nonresponse rate showed that it has a fair coefficient of determination of seventy three percent and a strong direct association of eighty five percent between the first and second visit of the TOTEX variable. The model also is a good fit to the data after passing the ANOVA test in determining the fit of the model. The DW statistics and the serial correction showed that the error residuals have a very small autocorrelation. It’s a possibility that there are certain variables that are omitted from the model. The normal probability plot indicates that the data is still not normal after logarithmic transformation has been made. However, the graph showed that the data didn’t deviate away from the straight line. The researcher expected these kinds of results because in reality and in the literature, the continuous variables are rarely normal and the distribution of the data is frequently lognormal even after many data transformation have been applied. As for the homoskedasticity, the graph of the predicted vs. the residual scores showed that majority of the observations is near the line. Moreover, there is no pattern in the graph indicating that the residual variances are equal.

Expenditure, 10% Nonresponse Rate, Second Imputation Class

Summary Statistics 0.884 0.782 0.781 4574.954 0.000 0.309

MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

Analysis of Variance (ANOVA) Sums of df Mean F Regress. 436.3063 1

p-level

436.3063 4574.954 0.00

Residual 121.8809 1278 0.0954 Total

558.1871

Durbin-Watson Test Normal Probability Plot Normal Probability Plot of Residuals Expected Normal Value

10 8 6 4 2 0 -2 -4 -6 -8 -2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

13.0

13.5

14.0

14.5

Residuals

Predicted vs. Residuals Predicted vs. Residual Scores

Residuals

Dependent variable: LNSV 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 9.5

10.0

10.5

11.0

11.5

12.0 Predicted Values

12.5

95% confidence

Expenditure, 10% Nonresponse Rate, Third Imputation Class Summary Statistics MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

0.9499 0.9023 0.9005 516.8993 0.0000 0.3314

Linearity of the model: Analysis of Variance (ANOVA) Sums of

df

Regress. 436.3063 1

Mean

F

p-level

436.3063 4574.954 0.00

Residual 121.8809 1278 0.0954 Total

558.1871

Independence of Error Terms: Durbin-Watson Test DW STAT

Serial

Estimate 2.043782 -0.022334 Normality of Error Terms: Normal Probability Plot Normal Probability Plot of Residuals 10 Expected Normal Value

8 6 4 2 0 -2 -4 -6 -8

-2.0

-1.5

-1.0

-0.5

0.0

0.5 Residuals

1.0

1.5

2.0

2.5

3.0

Equality of Error Variances: Predicted vs. Residuals Predicted vs. Residual Scores

Residuals

Dependent variable: LNSV 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 9.5

10.0

10.5

11.0

11.5

12.0

12.5

13.0

13.5

95% confidence

Predicted Values

Income, 10% Nonresponse Rate, First Imputation Class Summary Statistics MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

0.840 0.706 0.706 5703.605 0.000 0.331

Linearity of the model: Analysis of Variance (ANOVA) Sums of Regress. 625.0487 1

df

Mean

F

p-level

625.0487 5703.605 0.00

Residual 260.4915 2377 0.1096 Total

14.0

885.5402 Independence of Error Terms:

14.5

Durbin-Watson Test DW STAT

Serial

Estimate 2.047121 -0.023913 Normality of Error Terms: Normal Probability Plot Normal Probability Plot of Residuals Expected Normal Value

8 6 4 2 0 -2 -4 -6 -2.0

-1.0

-1.5

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Residuals

Equality of Error Variances: Predicted vs. Residuals Predicted vs. Residual Scores

Residuals

Dependent variable: LNSV 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 7

8

9

10

11

12

13 95% confidence

Predicted Values

Income Variable, 10% Nonresponse Rate, Second Imputation Class Summary Statistics MULTIPLE R MULTIPLE R2 ADJUSTED R

0.897 0.805 0.804

14

5261.480 0.000 0.331

F-STAT P-VALUE STD. ERR. OF ESTIMATE

Linearity of the Model: Analysis of Variance (ANOVA) Sums of

df

Regress. 576.7623 1

Mean

F

p-level

576.7623 5261.480 0.00

Residual 140.0941 1278 0.1096 Total

716.8564 Independence of Error Terms: Durbin-Watson Test DW STAT

Serial

Estimate 1.934528 0.031428 Normality of Error Terms: Normal Probability Plot Normal Probability Plot of Residuals Expected Normal Value

8 6 4 2 0 -2 -4 -6 -8 -2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

Residuals

Equality of Error Variances: Predicted vs. Residuals

1.0

1.5

2.0

2.5

Predicted vs. Residual Scores

Residuals

Dependent variable: LNSV 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 8

9

10

11

12

13

14 95% confidence

Predicted Values

Income Variable, 10% Nonresponse Rate, Third Imputation Class Summary Statistics MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

0.9591 0.9199 0.9185 642.9754 0.0000 0.3171

Linearity of the model: ANOVA Sums of df

Mean

F

p-level

Regress. 64.67059 1 64.67059 642.9753 0.000000 Residual 5.63249 56 0.10058 Total

70.30308 Independence of Error Terms: Durbin-Watson Test DW Stat

Serial

Estimate 2.157647 -0.079104 Normality of Error Terms:

15

Normal Probability Plot Normal Probability Plot of Residuals Expected Normal Value

5 4 3 2 1 0 -1 -2 -3 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Residuals

Independence of Error Terms: Predicted vs. Residuals

Predicted vs. Residual Scores

Residuals

Dependent variable: LNSV 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 10

11

12

13

14

15 95% confidence

Predicted Values

Expenditure, 20% Nonresponse Rate, First Imputation Class Summary Statistics MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

0.857 0.734 0.734 5786.271 0.000 0.273

LINEARITY OF THE MODEL: ANOVA Sums of Regress. 429.7392 1

df

Mean

F

p-level

429.7392 5786.271 0.00

16

Residual 155.8159 2098 0.0743 Total

585.5551 INDEPENDENCE OF ERROR TERMS: DURBIN-WATSON TEST Durbin-

Serial

Estimate 2.013534 -0.006859 NORMALITY OF ERROR TERMS: NORMAL PROBABILITY PLOT Normal Probability Plot of Residuals Expected Normal Value

10 8 6 4 2 0 -2 -4 -6 -8 -2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

13.0

13.5

Residuals

EQUALITY OF ERROR VARIANCES: PREDICTED vs. RESIDUALS Predicted vs. Residual Scores Dependent variable: LNSV 2.5 2.0

Residuals

1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0

9.0

9.5

10.0

10.5

11.0

11.5

12.0

12.5

95% confidence

Predicted Values

Expenditure, 20% Nonresponse Rate, Second Imputation Class Summary Statistics MULTIPLE R MULTIPLE R2

0.887 0.787

ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

0.787 4268.380 0.000 0.308

Linearity of the model: ANOVA Sums of Regress. 405.0530 1

df

Mean

F

405.0530 4268.380 0.00

Residual 109.3204 1152 0.0949 Total

p-level

514.3734 Independence of Error Terms: Durbin-Watson Test DW STAT

Serial

Estimate 2.014977 -0.007528

Normality of Error Terms: Normal Probability Plot

Normal Probability Plot of Residuals Expected Normal Value

10 8 6 4 2 0 -2 -4 -6 -8 -2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Residuals

Equality of Error Variances: Predicted vs. Residuals Predicted vs. Residual Scores

Residuals

Dependent variable: LNSV 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 9.5

10.0

10.5

11.0

11.5

12.0

12.5

13.0

13.5

14.0 95% confidence

Predicted Values

Expenditure, 20% Nonresponse Rate, Third Imputation Class Summary Statistics MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

0.9490 0.9006 0.8985 434.6591 0.0000 0.3336

Linearity of the Model: Analysis of Variance Sums of df

Mean

F

p-level

Regress. 48.36771 1 48.36771 434.6591 0.000000

14.5

Residual 5.34131 48 0.11128 Total

53.70902 Independence of Error Terms: Durbin-Watson Test Durbin-

Serial

Estimate 2.268400 -0.167040 Normality of Error Terms: Normal Probability Plot Normal Probability Plot of Residuals Expected Normal Value

3 2 1 0 -1 -2 -3 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Residuals

Equality of Error Variances: Predicted vs. Residuals Predicted vs. Residual Scores

Residuals

Dependent variable: LNSV 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 10.0

10.5

11.0

11.5

12.0

12.5

13.0

13.5

14.0

95% confidence

Predicted Values

Income, 20% Nonresponse Rate, First Imputation Class Summary Statistics MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

14.5

0.838 0.703 0.702 4954.234 0.000 0.331

15.0

Linearity of the Model: Analysis of Variance Sums of

df

Mean

Regress. 542.9226 1

F

p-level

542.9226 4954.233 0.00

Residual 229.9148 2098 0.1096 Total

772.8375

Independence of Error Terms: Durbin-Watson Test Durbin-

Serial

Estimate 1.985916 0.007035 Normality of Error Terms: Normal Probability Plot Normal Probability Plot of Residuals Expected Normal Value

8 6 4 2 0 -2 -4 -6 -1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Residuals

Equality of Error Variances: Predicted vs. Residuals Predicted vs. Residual Scores Dependent variable: LN SV 3.0 2.5

Residuals

2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 7

8

9

10 Predicted Values

11

12

13 95% confidence

14

Income, 20% Nonresponse Rate, Second Imputation Class Summary Statistics 0.906 0.821 0.821 5275.064 0.000 0.318

MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

Analysis of Variance Independence of Error Terms: Durbin-

Serial

Estimate 1.980753 0.008036 Normality of Error Terms: Normal Probability Plot Normal Probability Plot of Residuals Expected Normal Value

6 4 2 0 -2 -4 -6 -8 -2.5

-2.0

-1.5

-1.0

-0.5

0.0 Residuals

Equality of Error Variances: Predicted vs. Residuals

0.5

1.0

1.5

2.0

Predicted vs. Residual Scores

Residuals

Dependent variable: LN SV 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5

9

10

11

12

13

14 95% confidence

Predicted Values

Income, 20% Nonresponse Rate, Third Imputation Class Summary Statistics MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

0.9566 0.9151 0.9133 517.0385 0.0000 0.3277

Linearity of the Model: Analysis of Variance Sums of df

Mean

F

p-level

Regress. 55.51737 1 55.51737 517.0385 0.000000 Residual 5.15403 48 0.10738 Total

60.67140

Independence of Error Terms: Durbin-Watson Test Durbin-

Serial

Estimate 2.280743 -0.142227

Normality of Error Terms:

15

Normal Probability Plot Normal Probability Plot of Residuals Expected Normal Value

4 3 2 1 0 -1 -2 -3 -1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Residuals

Equality of Error Variances: Predicted vs. Residuals Predicted vs. Residual Scores

Residuals

Dependent variable: LN SV 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2

10

11

12

13

14

15 95% confidence

Predicted Values

Expenditure, 30% Nonresponse Rate, First Imputation Class Summary Statistics MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

0.840 0.705 0.705 4382.102 0.000 0.290

16

Linearity of the Model: Analysis of Variance Sums of

df

Regress. 367.4335 1

Mean

F

p-level

367.4335 4382.102 0.00

Residual 153.5270 1831 0.0838 Total

520.9605 Independence of Error Terms: Durbin-Watson Test Durbin-

Serial

Estimate 2.072061 -0.036173 Normality of Error Terms: Normal Probability Plot Normal Probability Plot of Residuals

Expected Normal Value

10 8 6 4 2 0 -2 -4 -6

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Residuals

Equality of Error Variances: Predicted vs. Residuals Predicted vs. Residual Scores

Residuals

Dependent variable: LNSV 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 9.0

9.5

10.0

10.5

11.0 Predicted Values

11.5

12.0

12.5

13.0 95% confidence

13.5

Expenditure, 30% Nonresponse Rate, Second Imputation Class Summary Statistics 0.890 0.791 0.791 3841.345 0.000 0.300

MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

Linearity of the Model: Analysis of Variance Sums of

df

Regress. 346.1192 1

Mean

F

p-level

346.1192 3841.345 0.00

Residual 91.1849 1012 0.0901 Total

437.3041 Independence of Error Terms: Durbin-Watson Test Durbin-

Serial

Estimate 2.023625 -0.012021 Normality of Error Terms: Normal Probability Plot Normal Probability Plot of Residuals Expected Normal Value

10 8 6 4 2 0 -2 -4 -6 -8 -2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

Residuals

Equality of Error Variances: Predicted vs. Residuals

1.5

2.0

2.5

3.0

Predicted vs. Residual Scores

Residuals

Dependent variable: LNSV 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 9.5

10.0

10.5

11.0

11.5

12.0

12.5

13.0

13.5 95% confidence

Predicted Values

Expenditure, 30% Nonresponse Rate, Third Imputation Class Summary Statistics MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

0.9425 0.8882 0.8856 333.7148 0.0000 0.3237

Linearity of the Model: Analysis of Variance Sums of df

Mean

F

p-level

Regress. 34.97366 1 34.97366 333.7148 0.000000 Residual 4.40164 42 0.10480 Total

39.37531

Independence of Error Terms: Durbin-Watson Test Durbin-

Serial

Estimate 2.589756 -0.326722

14.0

Normality of Error Terms: Normal Probability Plot Normal Probability Plot of Residuals Expected Normal Value

4 3 2 1 0 -1 -2 -3 -0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Residuals

Equality of Error Variances: Predicted vs. Residuals Predicted vs. Residual Scores

Residuals

Dependent variable: LNSV 1.2 1.0 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 10.0

10.5

11.0

11.5

12.0

12.5

13.0

14.0 95% confidence

Predicted Values

Income, 30% Nonresponse Rate, First Imputation Class Summary Statistics MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

13.5

0.845 0.713 0.713 4557.328 0.000 0.330

Linearity of the Model: Analysis of Variance

14.5

Sums of

df

Regress. 496.0775 1

Mean

F

p-level

496.0775 4557.328 0.00

Residual 199.3093 1831 0.1089 Total

695.3868

Independence of Error Terms: Durbin-Watson Test Durbin-

Serial

Estimate 2.094357 -0.047223

Normality of Error Terms: Normal Probability Plot

Normal Probability Plot of Residuals

Expected Normal Value

8 6 4 2 0 -2 -4 -6 -2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

12.5

13.0

13.5

3.0

Residuals

Equality of Error Variances: Predicted vs. Residuals Predicted vs. Residual Scores

Residuals

Dependent variable: LN SV 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 9.0

9.5

10.0

10.5

11.0

11.5 Predicted Values

12.0

95% confidence

Income, 30% Nonresponse Rate, Second Imputation Class

14.0

Summary Statistics MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

0.909 0.826 0.826 4793.392 0.000 0.310

Linearity of the Model: Analysis of Variance Sums of

df

Regress. 460.5995 1

Mean

F

p-level

460.5995 4793.392 0.00

Residual 97.2436 1012 0.0961 Total

557.8431

Independence of Error Terms: Durbin-Watson Test Durbin-

Serial

Estimate 2.072614 -0.038549

Normality of Error Terms: Normal Probability Plot Normal Probability Plot of Residuals Expected Normal Value

6 4 2 0 -2 -4 -6 -2.0

-1.5

-1.0

-0.5

0.0

0.5

Residuals

Equality of Error Variances: Predicted vs. Residuals

1.0

1.5

2.0

Predicted vs. Residual Scores Dependent variable: LN SV 2.0 1.5 Residuals

1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 9

10

11

12

13

14 95% confidence

Predicted Values

Income, 30% Nonresponse Rate, Third Imputation Class Summary Statistics MULTIPLE R MULTIPLE R2 ADJUSTED R F-STAT P-VALUE STD. ERR. OF ESTIMATE

0.9654 0.9319 0.9303 574.8240 0.0000 0.2753

Linearity of the Model: Analysis of Variance Sums of df

Mean

F

p-level

Regress. 43.55594 1 43.55594 574.8240 0.000000 Residual 3.18245 42 0.07577 Total

46.73840 Independence of Error Terms: Durbin-Watson Test Durbin-

Serial

Estimate 2.249448 -0.190671 Normality of Error Terms: Normal Probability Plot

15

Normal Probability Plot of Residuals

Expected Normal Value

3 2 1 0 -1 -2 -3 -4 -1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

Residuals

Equality of Error Variances: Predicted vs. Residuals Predicted vs. Residual Scores

Residuals

Dependent variable: LN SV 0.8 0.6 0.4 0.2 0.0 -0.2 -0.4 -0.6 -0.8 -1.0 10.0

10.5

11.0

11.5

12.0

12.5

13.0

13.5

14.0

14.5

15.0

95% confidence

Predicted Values

E. Comparison of Imputation Methods Variance Estimation and Biasness Measures of the effectiveness of the four imputation methods for imputing for the partial nonresponse data Expenditure Variable, 10% Nonresponse Rate METHODS

MD

MAD

RMSD

OMI HDI3 DRI3 SRI3

-6406.603632

56929.613669

108547.820041

-7204.560545 5363.466919

23839.817150 33683.480259

57726.615582 70553.643550

Income Variable, 10% Nonresponse Rate

METHODS

MD

MAD

RMSD

OMI HDI3 DRI3 SRI3

5978.393462

77502.270650

167206.240181

-11284.461504 9043.982223

32115.804981 51363.168122

77228.476946 106374.388796

Expenditure Variable, 20% Nonresponse Rate METHODS MD MAD RMSD OMI HDI3 DRI3 SRI3

METHODS OMI HDI3 DRI3 SRI3

-2497.141162

59555.355146

119193.320481

-7347.862975 5400.712813

23231.654338 33782.602655

53180.024322 72487.392833

Income Variable, 20% Nonresponse Rate MD MAD RMSD 14277.427361

87469.865623

244757.995335

-11059.090609 -9076.980826

35274.032863 57429.236572

114957.425614 148278.489381

Expenditure Variable, 30% Nonresponse Rate METHODS MD MAD RMSD OMI HDI3 DRI3 SRI3

742.526312

62388.111315

151740.940804

-7554.607707 1328.061322

24082.880071 32449.488519

59795.667757 72803.602152

Income Variable, 30% Nonresponse Rate METHODS MD MAD RMSD OMI HDI3 DRI3 SRI3

20310.908394

90396.258755

271775.351071

-13792.599597 1188.309972

34537.359021 51886.726288

103253.122885 131429.611649