Example 2 of Logistic Regression.5B7.5D Omnibus test

1 example 2 of logistic regression

1.1 dependent variable (coded dummy variable)
1.2 independent variables (coded dummy variables)
1.3 omnibus tests of model coefficients
1.4 variables in equation

example 2 of logistic regression

research subject: “the effects of employment, education, rehabilitation , seriousness of offense on re-arrest” [8]. social worker in criminal justice probation agency, tends examine whether of factors leading re-arrest of managed agency on past 5 years convicted , released. data consist of 1,000 clients following variables:

dependent variable (coded dummy variable)

• re-arrested vs. not re-arrested (0 = not re-arrested; 1 = re-arrested) – categorical, nominal

independent variables (coded dummy variables)

whether or not client adjudicated second criminal offense (1= adjudicated,0=not).
seriousness of first offense (1=felony vs. 0=misdemeanor) -categorical, nominal
high school graduate vs. not (0 = not graduated; 1 = graduated) - categorical, nominal
whether or not client completed rehabilitation program after first offense,0 = no rehab completed; 1 = rehab completed)-categorical, nominal
employment status after first offense (0 = not employed; 1 = employed)

note: continuous independent variables not measured on scenario.

the null hypothesis overall model fit: overall model not predict re-arrest. or, independent variables group not related being re-arrested. (and independent variables: of separate independent variables not related likelihood of re-arrest).

the alternative hypothesis overall model fit: overall model predicts likelihood of re-arrest. (the meaning respectively independent variables: having committed felony (vs. misdemeanor), not completing high school, not completing rehab program, , being unemployed related likelihood of being re-arrested).

logistic regression applied data on spss, since dependent variable categorical (dichotomous) , researcher examine odd ratio of potentially being re-arrested vs. not expected re-arrested.

omnibus tests of model coefficients

the table above shows omnibus test of model coefficients based on chi-square test, implies overall model predictive of re-arrest (we’re concerned row three—“model”): (4 degrees of freedom) = 41.15, p < .001, , null can rejected. testing null model, or group of independent variables taken together, not predict likelihood of being re-arrested. result means model of expecting re-arrestment more suitable data.

variables in equation

as shown on variables in equation table below, can reject null b coefficients having committed felony, completing rehab program, , being employed equal zero—they statistically significant , predictive of re-arrest. education level, however, not found predictive of re-arrest. controlling other variables, having committed felony first offense increases odds of being re-arrested 33% (p = .046), compared having committed misdemeanor. completing rehab program , being employed after first offense decreases odds or re-arrest, each more 50% (p < .001). last column, exp(b) (taking b value calculating inverse natural log of b) indicates odds ratio: probability of event occurring, divided probability of event not occurring. exp(b) value on 1.0 signifies independent variable increases odds of dependent variable occurring. exp(b) under 1.0 signifies independent variable decreases odds of dependent variable occurring, depending on decoding mentioned on variables details before. negative b coefficient result in exp(b) less 1.0, , positive b coefficient result in exp(b) greater 1.0. statistical significance of each b tested wald chi-square—testing null b coefficient = 0 (the alternate hypothesis not = 0). p-values lower alpha significant, leading rejection of null. here, independent variables felony, rehab, employment, significant ( p-value<0.05. examining odds ratio of being re-arrested vs. not re-arrested, means examine odds ratio comparison of 2 groups (re-arrested = 1 in numerator, , re-arrested = 0 in denominator) felony group, compared baseline misdemeanor group. exp(b)=1.327 “felony” can indicates having committed felony vs. misdemeanor increases odds of re-arrest 33%. “rehab” can having completed rehab reduces likelihood (or odds) of being re-arrested 51%.