The log transformation brings symmetry to the odds. Consider again the odds of agreeing to meet someone in person following an online interaction, 1360/9481=.143. Now consider the odds of not agreeing to meet someone in person following an online encounter, 9481/1360=6.971. If we take the log of these two odds we obtain -.843 and .843, respectively. The log odds (or logits) are modeled as a linear function of the predictors. In this case, one could use whether or not a teacher has discussed Internet safety as a predictor of the log odds of agreeing to meet with someone in person who has been met online. When the logistic regression is run, a parameter estimate for the predictor of -.297 is obtained, which is statistically significant (c2(1)=22.42, p=.0001). The interpretation of this parameter is that having a teacher discuss Internet safety decreases the predicted log odds of agreeing to meet with a stranger by .297 points. Since it is fairly difficult for most of us to think in terms of logs, the parameter is typically exponentiated (e-.297) which yields the odds ratio of .743. This ratio implies the odds of agreeing to meet with a stranger when a teacher has discussed Internet safety is only .743 times the odds of agreeing to meet with a stranger when no teacher has discussed Internet safety. Note that if the parameter in the logistic regression differs from 0, the odds ratio differs from 1, indicating the predictor is related to the odds of the outcome.

It is also possible to consider multiple predictors simultaneously. When multiple predictors are considered in a logistic regression model, the parameter estimate for a particular predictor is interpreted as a change in the predicted log odds of the outcome for a one unit change in the predictor, holding constant the other predictors in the model (Pedhazur, 1997). Again we can convert the parameter estimates into odds ratios, but these are referred to as adjusted odds ratios since they control for the other predictors in the model. To illustrate consider using logistic regression to examine the log odds of agreeing to meet with a stranger as a function of both having a teacher discuss internet safety and having a parent discuss internet safety. The results are presented in Table 1.

It is also possible to consider multiple predictors simultaneously. When multiple predictors are considered in a logistic regression model, the parameter estimate for a particular predictor is interpreted as a change in the predicted log odds of the outcome for a one unit change in the predictor, holding constant the other predictors in the model (Pedhazur, 1997). Again we can convert the parameter estimates into odds ratios, but these are referred to as adjusted odds ratios since they control for the other predictors in the model. To illustrate consider using logistic regression to examine the log odds of agreeing to meet with a stranger as a function of both having a teacher discuss internet safety and having a parent discuss internet safety. The results are presented in Table 1.

Table 1.
Logistic regression predicting log odds of agreeing to meet with a stranger based on whether or not there was discussion with a teacher and whether or not there was a discussion with a parent

	Parameter	SE	x2	p-value	adjusted odds ratio
Intercept	-1.785	.0503	1258.44	.0001
Teacher*	-.2746	.0644	18.16	.0001	.760
Parent*	-.0965	.0626	2.37	.1232	.908
* having a discussion is coded 1, not having a discussion is coded 0

The adjusted odds ratio for the teacher discussion predictor is .76. This indicates that after controlling for whether or not there has been a discussion of internet safety with the parent, those who have discussed internet safety with a teacher have odds of meeting with a stranger that are only .76 times the odds of those who have not discussed internet safety with the teacher.

It is also possible to consider the interaction between predictors. Consider a logistic regression where the log odds of agreeing to meet with a stranger are modeled as a function of discussing Internet safety with a teacher, discussing Internet safety with a parent, and the interaction of these two predictors. The results are presented in Table 2.

Table 2.
Logistic regression predicting log odds of agreeing to meet with a stranger based on whether or not there was discussion with a teacher, whether or not there was a discussion with a parent, and the interaction of the two predictors.

	Parameter	SE	x2	p-value	adjusted odds ratio
Intercept	-1.744	.0531	1079.99	.0001
Teacher*	-.5455	.1425	14.66	.0001	.580
Parent*	-.1685	.0706	5.70	.0169	.845
T*P	.3489	.1602	4.74	.0294	1.418
* having a discussion is coded 1, not having a discussion is coded 0

The interaction is statistically significant, leading us to conclude that the effect of teacher discussion on the predicted log odds depends on whether or not there was a parent discussion. If there was no parent discussion, the odds ratio for the teacher discussion variable is .580. If there was parent discussion, the odds ratio for the teacher discussion variable is .822 (.580*1.418). In both cases having discussed Internet safety with a teacher reduces the predicted odds of agreeing to meet with a stranger. The effect of teacher discussion, however, is greater when there has been no discussion with a parent.