Odds Ratio in Logistic Regression

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In logistic regression, odds ratio indicates the nature and the degree of association between a dependent variable and independent variables. Macdonald (2015) states that odds ratio applies to the prediction of a dependent variable using independent variables in logistic regression analysis. In this case, the dependent variable is burnout while the independent variables are coping style and stress from teaching.

The dependent variable is a binary categorical variable because it comprises burnout and no burnout. The independent variables contain continuous data, which indicate the degree of coping style and stress from teaching. High scores and low scores of coping style indicate high and low ability to cope with stress respectively.

Similarly, high scores and low scores of stress from teaching show high and low levels of stress that emanate from teaching. The odds ratio in this case originates from the comparison of the probability of burnout and the probability of no burnout. In this view, the logistic analysis applies these variables in demonstrating odds ratio.

Table 1 indicates that there is significant difference between logistic regression model with a constant only and the logistic regression model with all independent variables, namely, coping style and stress from teaching, (χ²(2) = 137, p = 0.000).

Table 1. Omnibus Tests of Model Coefficients

		Chi-square	df	Sig.
Step 1	Step	137.015	2	.000
	Block	137.015	2	.000
	Model	137.015	2	.000

Table 2

Model Summary
Step	-2 Log likelihood	Cox & Snell R Square	Nagelkerke R Square
1	393.092	.254	.375

The model summary table (Table 2) shows that coping style and stress from teaching explain 25.4% (Cox & Snell R Square) or 37.5% (Nagelkerke R Square) of the variation in burnout. The explanatory power is important in interpreting odds ratio, which describe the nature and the strength of the relationship between burnout, the dependent variable, and coping style and stress from teaching, the independent variables.

Table 3. Classification Table

	Observed		Predicted
			Burnout		Percentage Correct
			Not Burnt Out	Burnt Out
Step 1	Burnout	Not Burnt Out	320	28	92.0
		Burnt Out	65	54	45.4
	Overall Percentage				80.1

Table 3 is a contingency table, which shows the distribution for 80.1% of the total lecturers (N = 467). In this view, the table suggests that the model can predict 80.1% of the total lecturers, which is very significant.

From the logistic regression model, it is evident that coping style (Wald χ²(1) = 71.287, p = 0.000) and stress from teaching (Wald χ²(1) = 5.760, p = 0.016) are significant predictors of burnout. Thus, the statistical significance of coping style and stress from teaching validates the use of these predictors in the analysis of odds ratio.

In interpreting odds ratio, Field (2013) states that odds ratio greater than one indicates that a predictor variable increases a criterion variable while odds ratio less than one indicates that the predictor variable reduces criterion variable. From Table 4, the odds ratio for coping style and burnout is 1.111 (95% CI, 1.084 to 1.138).

The odds ratio suggests that a unit increase in coping ability increases burnout by 11.1%. The odds ratio for stress from teaching and burnout is 0.968 (95% CI, 0.943 to 0.994). The odds ratio suggests that a unit increase in stress from teaching results in a reduction of burnout by 3.2%.

Table 4. Variables in the Equation
a. Variable(s) entered on step 1: cope, teaching.

		B	S.E.	Wald	df	Sig.	Exp(B)	95% C.I. for EXP(B)
		B	S.E.	Wald	df	Sig.	Exp(B)	Lower	Upper
Step 1^a	Cope	.105	.012	71.287	1	.000	1.111	1.084	1.138
	Teaching	-.032	.013	5.760	1	.016	.968	.943	.994
	Constant	-2.077	.592	12.308	1	.000	.125

References

Field, A. (2013). Discovering statistics using SPSS (4th ed.). London: SAGE Publisher.

Macdonald, S. (2015). Essentials of Statistics with SPSS. Raleigh: Lulu.com Publisher.

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Odds Ratio in Logistic Regression

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