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# Multiple logistic regression in SPSS

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Question 2: Multiple logistic regression

The model presented below is an extension of the simple logistic model above, except that there are now two predictors of 'expire': 'blunt' and 'iss.' ISS is a continuous variable that is a measure of trauma severity.

Case Processing Summary
Unweighted Cases N Percent
Selected Cases Included in Analysis 859 99.8
Missing Cases 2 .2
Total 861 100.0
Unselected Cases 0 .0
Total 861 100.0
a If weight is in effect, see classification table for the total number of cases.

Categorical Variables Codings
Frequency Parameter coding
(1)
BLUNT .00 499 .000
1.00 360 1.000

Omnibus Tests of Model Coefficients
Chi-square df Sig.
Step 1 Step 338.581 2 .000
Block 338.581 2 .000
Model 338.581 2 .000

Model Summary
Step -2 Log likelihood Cox & Snell R Square Nagelkerke R Square
1 688.460 .326 .467

Hosmer and Lemeshow Test
Step Chi-square df Sig.
1 43.790 8 .000

Contingency Table for Hosmer and Lemeshow Test
EXPIRED = .00 EXPIRED = 1.00 Total
Observed Expected Observed Expected
Step 1 1 118 114.582 0 3.418 118
2 40 39.386 1 1.614 41
3 103 100.052 4 6.948 107
4 86 79.960 1 7.040 87
5 75 74.722 12 12.278 87
6 71 81.369 37 26.631 108
7 55 55.131 29 28.869 84
8 33 40.722 52 44.278 85
9 19 23.749 69 64.251 88
10 14 4.320 40 49.680 54

Classification Table
Predicted
EXPIRED Percentage Correct
Observed .00 1.00
Step 1 EXPIRED .00 556 58 90.6
1.00 111 134 54.7
Overall Percentage 80.3
a The cut value is .500

Variables in the Equation
B S.E. Wald df Sig. Exp(B)
Step 1 BLUNT(1) .874 .206 18.003 1 .000 2.397
ISS .106 .009 125.831 1 .000 1.111
Constant -3.618 .230 246.729 1 .000 .027
a Variable(s) entered on step 1: BLUNT, ISS.

Fully discuss the model multiple logistic regression shown above, including assessment of the significance of the model, the R-square, the significance of the continuous predictor and the Hosmer-Lemeshow goodness of fit test), as well as your interpretation of the model (i.e., what are the 'real-world' implications of what you found in your model?); compare this multiple logistic regression to the simple regression obtained for Question 1: did the addition of a continuous predictor improve the model? Did the inclusion of a continuous predictor (i.e., ISS) change the significance of the binary predictor (i.e., blunt)?
Summary of the Trauma Database:
The dataset for this problem contains 861 Trauma Alert Red cases (highest level of alert) collected over a nearly 5-year period. The variables included are:

&#61656; EXPIRED: the outcome variable; a dummy variable taking the value of 1 if the patient did not survive and 0 if the patient lived
&#61656; AGE: age of patient (range is from 14 to 92)

&#61656; GCS: Glasgow Coma Score (range is from 3 to 15, with lower scores indicating more severe injury)

&#61656; ISS: Injury Severity Score (range is from 1 to 75, with higher score indicating more severe injury)

&#61656; RTS: Revised Trauma Score (range is from 0 to 7.84, with lower score indicating more severe injury)

&#61656; INJDAY: A dummy (or indicator) variable that takes the value of 1 if the case presented in the ER between 6a and 6p on a weekday and zero otherwise

&#61656; BLUNT: A dummy variable that takes the value of 1 if the mechanism of injury was blunt trauma and 0 if the mechanism was penetrating

&#61656; MALE: A dummy variable for gender; takes the value of 1 for male and 0 for female

&#61656; INTUBATE: A dummy variable for intubation status; takes the value 1 if patient was intubated and 0 if not

&#61656; RGCS: 'revised' GCS; I subtracted 3 from this variable and then divided this difference by 12. This transforms the variable so that instead of a range of 3-15 (like the GCS), it has a range of 0-1, with scores closer to 0 indicating more severe injury

RRTS: 'revised' RTS; I divided this variable by 7.84. This transforms the variable so that instead of a range of 0-7.84 (like RTS), it has a range of 0-1, with scores closer to 0 indicating more severe injury

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#### Solution Preview

Please see the attachments .SPSS out put (Version 17 also included)

Logistic regression
Binomial (or binary) logistic regression is a form of regression which is used when the dependent is a dichotomy and the independents are of any type. Here EXPIRED is taken as the dependent variable. This variable is coded as binary. The independent variables considered is BLUNT and ISS. Logistic regression can be used to predict a dependent variable on the basis of continuous and/or categorical independents and to determine the percent of variance in the dependent variable explained by the independents. Logistic regression makes no assumption about the distribution of the independent variables. They do not have to be normally distributed, linearly related or of equal variance within each group. The impact of predictor variables is usually explained in terms of odds ratios.
Variables in the logistic regression model
Variable Data Type Values
Dependent Y EXPIRED Binary 0,1
Independent X1 BLUNT Dummy variable 0,1
Independent X2 ISS Continuous

The dependent variable in logistic regression is usually dichotomous, that is, the dependent variable can take the value 1 ...

#### Solution Summary

The solution provides step by step method for the calculation of multiple logistic regression in SPSS . Formula for the calculation and Interpretations of the results are also included.

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