Question

Consider the following three variables.

Variable Coding Label

DRINK 1 = yes 2 = no Regular Drinker

SEX 1 = male 2 = female

CASES 0 = Normal 1 = Case of Depression Depressed is cesd > 16s:

Α logistic regression model using DRINK as the dependent variable and CASES and SEX as independent variables and the the appropriate interaction term was fit to the data. Logistic regression output is as follows:

Logistic regression Number of obs = 294

LR chi2(3) = 5.62

Prob > chi2 = 0.1318

Log likelihood = -145.95772 Pseudo R2 = 0.0189

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drink01 | Coef. Std. Err. z P>|z| [95% Conf. Interval]

-------------+------------------------------------------------------------------------------------------------------------

cases | -.4405564 .8413815 -0.52 0.601 -2.089634 1.208521

female | -.7743296 .3455196 -2.24 0.025 -1.451536 -.0971237

fem_case | .9386327 .9578851 0.98 0.327 -.9387877 2.816053

constant | 1.826851 .2879632 6.34 0.000 1.262453 2.391248

i. State the mathematical formula of the fitted model

ii. Is the interaction term significant

iii. What are the Woman to Man Odds Ratio (OR) for Depressed and Non-depressed persons?

Answer 1

i.

From the regression output summary, the regression equation is defined as,

ii.

For the interaction term,

P-value = 0.327

Since the P-value < 0.05 at a 5% significance level, the null hypothesis is not rejected hence we can conclude that the interaction of females and cases has no significant effect on DRINK.

iii.

For Depressed (Cases = 1)

The odd ratio of women compared to men is obtained as follows,

For women (Female = 1)

For men (female = 0)

The Odd ration of women compared to men among depressed is,

For Non-Depressed (Cases = 0)

The odd ratio of women compared to men is obtained as follows,

For women (Female = 1)

For men (female = 0)

The Odd ration of women compared to men among non-depressed,