Example 1 of Logistic Regression .5B3.5D Omnibus test

1 example 1 of logistic regression

1.1 independent variables
1.2 dependent variable

1.2.1 block 1: method = forward stepwise (conditional)
1.2.2 omnibus tests of model coefficients
1.2.3 block 2: method = forward stepwise (conditional)
1.2.4 omnibus tests of model coefficients
1.2.5 variables in equation

example 1 of logistic regression

spector , mazzeo examined effect of teaching method known psi on performance of students in course, intermediate macro economics. question whether students exposed method scored higher on exams in class. collected data students in 2 classes, 1 in psi used , in traditional teaching method employed. each of 32 students, gathered data on

independent variables

• gpa-grade point average before taking class. • tuce-the score on exam given @ beginning of term test entering knowledge of material. • psi- dummy variable indicating teaching method used (1 = used psi, 0 = other method).

dependent variable

• grade — coded 1 if final grade a, 0 if final grade b or c.

the particular interest in research whether psi had significant effect on grade. tuce , gpa included control variables.

statistical analysis using logistic regression of grade on gpa, tuce , psi conducted in spss using stepwise logistic regression.

in output, block line relates chi-square test on set of independent variables tested , included in model fitting. step line relates chi-square test on step level while variables included in model step step. note in output step chi-square, same block chi-square since both testing same hypothesis tested variables enter on step non-zero. if doing stepwise regression, however, results different. using forward stepwise selection, researchers divided variables 2 blocks (see method on syntax following below).

logistic regression var=grade

/method=fstep psi / fstep gpa tuce

/criteria pin(.50) pout(.10) iterate(20) cut(.5).

the default pin value .05, changed researchers .5 insignificant tuce make in. in first block, psi alone gets entered, block , step chi test relates hypothesis h0: βpsi = 0. results of omnibus chi-square tests implies psi significant predicting grade more final grade of a.

block 1: method = forward stepwise (conditional)
omnibus tests of model coefficients

then, in next block, forward selection procedure causes gpa entered first, tuce (see method command on syntax before).

block 2: method = forward stepwise (conditional)
omnibus tests of model coefficients

the first step on block2 indicates gpa significant (p-value=0.003<0.05, α=0.05)

so, looking @ final entries on step2 in block2,

the step chi-square, .474, tells whether effect of variable entered in final step, tuce, differs zero. equivalent of incremental f test of parameter, i.e. tests h0: βtuce = 0.
the block chi-square, 9.562, tests whether either or both of variables included in block (gpa , tuce) have effects differ zero. equivalent of incremental f test, i.e. tests h0: βgpa = βtuce = 0.
the model chi-square, 15.404, tells whether of 3 independent variabls has significant effects. equivalent of global f test, i.e. tests h0: βgpa = βtuce = βpsi = 0.

tests of individual parameters shown on variables in equation table , wald test (w=(b/sb)2, b β estimation , sb standard error estimation ) testing whether individual parameter equals 0 . can, if want, incremental lr chi-square test. that, in fact, best way it, since wald test referred next biased under situations. when parameters tested separately, controlling other parameters, see effects of gpa , psi statistically significant, effect of tuce not. both have exp(β) greater 1, implying probability grade greater getting other grade depends upon teaching method psi , former grade average gpa.

variables in equation

a. variable(s) entered on step 1: psi