Project 4:

The California Bureau of Prison's board of directors wanted to be able to predict parole violations (DV) by prison punishment record (IV) and prior criminal record (IV). Information on 4000 inmates of the state penitentiary system from 1989 - 1994 records was scrubbed. Columns are coded as follows.

Incidence of Parole Violation, by punishment record and a prior criminal record for 4000 inmates of California State penitentiary system from 1989- 1994.

• Punishment record in prison 0=None, 1=1-2 times, 2=3 or more times
• Prior record 0=none, 1=fine/probation, 2=reform school, 3=jail, 4=penitentiary
• Subsequent parole violation 0=No, 1=Yes */ Number of inmates

Use the Checklist (Table 10.16) found on page 482 of the textbook and the information provided below to write a report on the Logistic Regression for the data set provided. (Hint: Report should be similar in scope to "Results at the end of Chapter 10".

Logistic Regression Output

Logistic Regression

Case Processing Summary
Unweighted Casesa	N	Percent
Selected Cases	Included in Analysis	4000	100.0
Missing Cases	0	.0
Total	4000	100.0
Unselected Cases	0	.0
Total	4000	100.0
a. If weight is in effect, see classification table for the total number of cases.
Dependent Variable Encoding
Original Value	Internal Value
No	0
Yes	1

Categorical Variables Codings
	Frequency	Parameter coding
(1)	(2)	(3)	(4)
Prior Record	None	2540	1.000	.000	.000	.000
Fine/Probation	356	.000	1.000	.000	.000
Reform School	448	.000	.000	1.000	.000
Jail	440	.000	.000	.000	1.000
Penitentiary	216	.000	.000	.000	.000
Prison Punish Rec.	None	2468	1.000	.000
1-2 Times	956	.000	1.000
3 or More Times	576	.000	.000

Block 0: Beginning Block

Classification Tablea,b
	Observed	Predicted
	Subseq Parole Violations	Percentage Correct
	No	Yes
Step 0	Subseq Parole Violations	No	2924	0	100.0
Yes	1076	0	.0
Overall Percentage			73.1
a. Constant is included in the model.
b. The cut value is .500
Variables in the Equation
	B	S.E.	Wald	df	Sig.	Exp(B)
Step 0	Constant	-1.000	.036	786.087	1	.000	.368
Variables not in the Equation
	Score	df	Sig.
Step 0	Variables	PPUNREC	72.685	2	.000
PPUNREC(1)	72.259	1	.000
PPUNREC(2)	31.225	1	.000
PRREC	117.669	4	.000
PRREC(1)	94.508	1	.000
PRREC(2)	.001	1	.976
PRREC(3)	51.526	1	.000
PRREC(4)	18.399	1	.000
Overall Statistics	161.998	6	.000

Block 1: Method = Enter

Omnibus Tests of Model Coefficients
	Chi-square	df	Sig.
Step 1	Step	157.367	6	.000
Block	157.367	6	.000
Model	157.367	6	.000
Model Summary
Step	-2 Log-likelihoodthe	Cox & Snell R Square	Nagelkerke R Square
1	4500.727a	.039	.056
a. Estimation terminated at iteration number 4 because parameter estimates changed by less than .001.
Classification Tablea
	Observed	Predicted
	Subseq Parole Violations	Percentage Correct
	No	Yes
Step 1	Subseq Parole Violations	No	2924	0	100.0
Yes	1076	0	.0
Overall Percentage			73.1
a. The cut value is .500
Variables in the Equation
	B	S.E.	Wald	df	Sig.	Exp(B)
Step 1a	PPUNREC			44.853	2	.000
PPUNREC(1)	-.498	.102	23.712	1	.000	.608
PPUNREC(2)	-.002	.113	.000	1	.983	.998
PRREC			87.301	4	.000
PRREC(1)	-.807	.148	29.571	1	.000	.446
PRREC(2)	-.575	.184	9.734	1	.002	.563
PRREC(3)	.019	.170	.013	1	.911	1.019
PRREC(4)	-.209	.172	1.480	1	.224	.811
Constant	-.149	.158	.896	1	.344	.861
a. Variable(s) entered on step 1: PPUNREC, PRREC.

SEQUENTIAL LOGISTIC REGRESSION OUTPUT

Logistic Regression

Case Processing Summary
Unweighted Casesa	N	Percent
Selected Cases	Included in Analysis	4000	100.0
Missing Cases	0	.0
Total	4000	100.0
Unselected Cases	0	.0
Total	4000	100.0
a. If weight is in effect, see classification table for the total number of cases.

Dependent Variable Encoding
Original Value	Internal Value
No	0
Yes	1

Categorical Variables Codings
	Frequency	Parameter coding
(1)	(2)	(3)	(4)
Prior Record	None	2540	1.000	.000	.000	.000
Fine/Probation	356	.000	1.000	.000	.000
Reform School	448	.000	.000	1.000	.000
Jail	440	.000	.000	.000	1.000
Penitentiary	216	.000	.000	.000	.000
Prison Punish Rec.	None	2468	1.000	.000
1-2 Times	956	.000	1.000
3 or More Times	576	.000	.000

Block 0: Beginning Block

Classification Tablea,b

Observed

Predicted

Subseq Parole Violations

Percentage Correct

No

Yes

Step 0

Subseq Parole Violations

No

2924

0

100.0

Yes

1076

0

.0

Overall Percentage

73.1

a. Constant is included in the model.

b. The cut value is .500

Variables in the Equation

B

S.E.

Wald

df

Sig.

Exp(B)

Step 0

Constant

-1.000

.036

786.087

1

.000

.368

Variables not in the Equation
	Score	df	Sig.
Step 0	Variables	PPUNREC	72.685	2	.000
PPUNREC(1)	72.259	1	.000
PPUNREC(2)	31.225	1	.000
Overall Statistics	72.685	2	.000

Block 1: Method = Enter

Omnibus Tests of Model Coefficients
	Chi-square	df	Sig.
Step 1	Step	71.516	2	.000
Block	71.516	2	.000
Model	71.516	2	.000
Model Summary
Step	-2 Log-likelihood	Cox & Snell R Square	Nagelkerke R Square
1	4586.577a	.018	.026
a. Estimation terminated at iteration number 4 because parameter estimates changed by less than .001.
Classification Tablea
	Observed	Predicted
	Subseq Parole Violations	Percentage Correct
	No	Yes
Step 1	Subseq Parole Violations	No	2924	0	100.0
Yes	1076	0	.0
Overall Percentage			73.1
a. The cut value is .500
Variables in the Equation
	B	S.E.	Wald	df	Sig.	Exp(B)
Step 1a	PPUNREC			71.739	2	.000
PPUNREC(1)	-.653	.100	42.921	1	.000	.520
PPUNREC(2)	-.067	.111	.370	1	.543	.935
Constant	-.601	.087	47.552	1	.000	.548
a. Variable(s) entered on step 1: PPUNREC.

Block 2: Method = Enter

Omnibus Tests of Model Coefficients
	Chi-square	df	Sig.
Step 1	Step	85.850	4	.000
Block	85.850	4	.000
Model	157.367	6	.000
Model Summary
Step	-2 Log-likelihood were	Cox & Snell R Square	Nagelkerke R Square
1	4500.727a	.039	.056
a. Estimation terminated at iteration number 4 because parameter estimates changed by less than .001.

Classification Tablea
	Observed	Predicted
	Subseq Parole Violations	Percentage Correct
	No	Yes
Step 1	Subseq Parole Violations	No	2924	0	100.0
Yes	1076	0	.0
Overall Percentage			73.1
a. The cut value is .500
Variables in the Equation
	B	S.E.	Wald	df	Sig.	Exp(B)
Step 1a	PPUNREC			44.853	2	.000
PPUNREC(1)	-.498	.102	23.712	1	.000	.608
PPUNREC(2)	-.002	.113	.000	1	.983	.998
PRREC			87.301	4	.000
PRREC(1)	-.807	.148	29.571	1	.000	.446
PRREC(2)	-.575	.184	9.734	1	.002	.563
PRREC(3)	.019	.170	.013	1	.911	1.019
PRREC(4)	-.209	.172	1.480	1	.224	.811
Constant	-.149	.158	.896	1	.344	.861
a. Variable(s) entered on step 1: PRREC.

ROC Curve

Case Processing Summary
Subseq Parole Violations	Valid N (listwise)
Positivea	1076
Negative	2924
Larger values of the test result variable(s) indicate stronger evidence for a positive actual state.
a. The positive actual state is Yes.

Area Under the Curve
Test Result Variable(s)	Area	Std. Errora	Asymptotic Sig.b	Asymptotic 95% Confidence Interval
Lower Bound	Upper Bound
Prison Punish Rec.	.575	.010	.000	.555	.595
Prior Record	.590	.010	.000	.569	.610
Predicted probability	.620	.010	.000	.600	.640
The test result variable(s): Prison Punish Rec., Prior Record, Predicted probability has at least one tie between the positive actual state group and the negative actual state group. Statistics may be biased.
a. Under the nonparametric assumption
b. Null hypothesis: true area = 0.5

Univariate Statistics
	N	Missing
Count	Percent
PPUNREC	4000	0	.0
PRREC	4000	0	.0
SUBPARVIO	4000	0	.0

Regression

Variables Entered/Removeda
Model	Variables Entered	Variables Removed	Method
1	Prior Record, Prison Punish Rec.b	.	Enter
a. Dependent Variable: Subseq Parole Violations
b. All requested variables entered.

Model Summary
Model	R	R Square	Adjusted R Square	Std. Error of the Estimate
1	.187a	.035	.034	.436
a. Predictors: (Constant), Prior Record, Prison Punish Rec.

ANOVAa
Model	Sum of Squares	df	Mean Square	F	Sig.
1	Regression	27.460	2	13.730	72.294	.000b
Residual	759.096	3997	.190
Total	786.556	3999
a. Dependent Variable: Subseq Parole Violations
b. Predictors: (Constant), Prior Record, Prison Punish Rec.
Coefficientsa
Model	Unstandardized Coefficients	Standardized Coefficients	t	Sig.	Collinearity Statistics
B	Std. Error	Beta	Tolerance	VIF
1	(Constant)	.195	.009		21.019	.000
Prison Punish Rec.	.062	.010	.102	6.446	.000	.968	1.033
Prior Record	.048	.005	.139	8.828	.000	.968	1.033
a. Dependent Variable: Subseq Parole Violations
Collinearity Diagnosticsa
Model	Dimension	Eigenvalue	Condition Index	Variance Proportions
(Constant)	Prison Punish Rec.	Prior Record
1	1	2.059	1.000	.10	.10	.10
2	.556	1.925	.00	.50	.67
3	.385	2.311	.90	.40	.22
a. Dependent Variable: Subseq Parole Violations

Logistic Regression Subsequent Parole Violation as a function of Prior Punishment Received and Prior Record.

Variables in the Equation
	B	S.E.	Wald	df	Sig.	Exp(B)
Step 1a	PPUNREC			44.853	2	.000
PPUNREC(1)	-.498	.102	23.712	1	.000	.608
PPUNREC(2)	-.002	.113	.000	1	.983	.998
PRREC			87.301	4	.000
PRREC(1)	-.807	.148	29.571	1	.000	.446
PRREC(2)	-.575	.184	9.734	1	.002	.563
PRREC(3)	.019	.170	.013	1	.911	1.019
PRREC(4)	-.209	.172	1.480	1	.224	.811
Constant	-.149	.158	.896	1	.344	.861
a. Variable(s) entered on step 1: PPUNREC, PRREC.

PAGE482

TABLE 10.16 Checklist for Standard Logistic Regression with Dichotomous Outcome

1. Issues

a. Ratio of cases to variables and missing data

b. Adequacy of expected frequencies (if necessary)

c. Outliers in the solution (if fit inadequate)

d. Multicollinearity

e. Linearity in the logit

2. Major analysis

a. Evaluation of overall fit. If adequate:

(1)Significance tests for each predictor

(2)Parameter estimates

b. Effect size for model

c. Evaluation of models without predictors

3. Additional analyses

a. Odds ratios

b. Classification or prediction success table

Results

A direct logistic regression analysis was performed on work status as the outcome and four attitudinal predictors: locus of control, attitude toward current marital status, attitude toward womens role, and attitude toward housework. Analysis was performed using SAS LOGISTIC. Twenty-two cases with missing values on continuous predictors were imputed using the EM algorithm through SPSS MVA after finding no statistically significant deviation from randomness using Littles MCAR test, p = .331. After the deletion of three cases with missing values, data from 462 women were available for analysis: 217 housewives and 245 women who work outside the home more than 20 hours a week for pay. A test of the full model with all four predictors against a constant-only model was statistically significant, 2(4, N = 440) = 23.24, p < .001, indicating that the predictors, as a set, significantly distinguished between working women and housewives. The variance in work status accounted for is small, however, with Somers's D = .263, with a 95% confidence interval for the effect size of .07 ranging from .02 to .12 using Steiger and Fouladis (1992) R2 software. The classification was unimpressive, with 67% of the working women and 48% of the housewives correctly predicted, for an overall success rate of 58%. Table 10.15 shows regression coefficients, Wald statistics, odds ratios, and 95% confidence intervals for odds ratios for each of the four predictors. According to the Wald criterion, only attitude toward the role of women significantly predicted work status, 2(1, N = 440) = 19.30, p < .001. A model run with attitude toward the role of women omitted was not significantly different from a constant-only model; however, this model was significantly different from the full model, 2 (1, N = 440) = 20.47, p < .001. This confirms the finding that attitude toward womens role is the only statistically significant predictor of work status among the four attitudinal variables. However, the odds ratio of .93 shows little change in the likelihood of working on the basis of a one-unit change in attitude toward womens role. Thus, attitude towards the proper role of women in society distinguishes between women who do and do not work outside the home at least 20 hours per week, but the distinction is not a very strong one.