Binary Logistic Regression

Also interesting to investigate are the factors affecting the respondents’ switching decisions.

To do so, a binary logistic regression was run to identify any variables impacting switching behavior. A binary logit model has a two-category dependent variable, indicating whether an event has occurred or not. In this case, the dependent variable is DSWITCH, indicating whether respondents switch their preferred pricing alternative from the fixed price alternative in choice 1 to the time of use or peak-load prices in choice 2. A value of 1 for the dependent variable will be the target group, meaning that the switch occurs, and 0 if the switch does not occur. The probability of a respondent i switching his or her preferred pricing alternative is expressed in equation 7.1.

Prob(Switch) = ^Exp(Xiβ)

1+Exp(X_𝑖𝑖β) (7.1)

Equation 7.1 can also be expressed as:

Log � Prob (switch)

1-Prob (switch)� = β₀+β₁X₁+…+β_nX_n+ ε_i (7.2)

Where prob (switch) is the probability that a respondent switches preferred pricing alternative from fixed price in the first choice to time of use or peak-load price in choice 2, β₀ is the intercept and the other βs are coefficients associated with the independent X variables, and ε_i is a disturbance term (Ezebilo & Animasaun, 2011). The results from the binary logistic regression model are shown in table 7.6. The table reports the coefficient for the independent variables in the β – column, indicating the direction of the probability. The p-value reports on the statistical significance of the estimate, and the exp (β) reports the odds ratio.

The odds ratio explains the amount of change in odds of switching for every one-unit increase in the predictor variables. If a coefficient β is positive, the odds ratio will be larger than one, if the coefficient is equal to zero, the odds ratio will be one and if a coefficient is negative, the odds ratio will be less than one but still positive.

Table 7.6 - Binary Logistic Regression

Positive values for the coefficients indicate that an increase in the predictor variable will increase the likelihood of switching. With a negative value, the likelihood of falling into the reference group is decreasing as the score on the predictor variable increases. This is true for the continuous variables. For the dummy variables, a positive coefficient will imply that the group coded 1 for that variable will be more likely to switch, and a negative value will indicate that this group will be less likely to switch.

For overall fit of the model, the chi² test reports on the statistical significance of the model, compared to a model including only the constant. As seen in table 7.6, the model is statistically significant in terms of the low chi² value of .000, meaning that the model fits significantly better than a model with no predictor variables. The model also reported pseudo r² values. The Cox & Snell r² was .140, while the Nagelkerke r² was .251. These values represent an analogy to the r² values typically obtained in OLS regression. These two values

can therefore be interpreted to say that the model explains approximately 14% to 25.1% of the variation in the model outcome.

From the results, it is seen that the variables DTREATMENT, INC, INC², DOWN and DLELUSE are significant at the 5% level, while the variable DIMEE is significant at the 10%

level. Further, the variables EDUC and EDUC² are statistically significant at the 1% level.

The variable DTREATMENT has a negative coefficient; meaning that a person receiving the environmental and system benefits information treatment is less likely to switch preferred pricing alternative from fixed price in the first choice to time of use or peak-load in the second choice, compared to those who did not receive the treatment. The odds ratio is .452, meaning that respondents receiving the treatment are approximately 55% less likely to make the switch.

The EDUC variable has a positive coefficient, while EDUC² is negative. This indicates that an increase in respondents’ years of education will have a positive effect on the probability of switching, but only up to a certain point. Beyond this point, the EDUC² variable indicates that the probability of switching no longer increases with increased education, but starts to decrease. The model also shows some income effects, with positive coefficients on INC and INC². This indicates that as income increases by a unit, the probability of switching will increase. The income-squared variable indicates that this relationship may not be linear, and can change in direction at some level of income.

The variable for home ownership has a negative coefficient, meaning that homeowners are less likely than those who are not homeowners to switch from the fixed price to any of the two other alternatives. The odds ratio of .366 indicates that homeowners are approximately 63% less likely to make the switch. Further, the variable indicating low monthly electricity use had a negative coefficient. This means that those who use less electricity are less likely to switch from fixed price to the time of use price or the peak-load price. The odds ratio of .362 reveals that those with low electricity use are roughly 64% less likely to switch than those who are not in the low electricity category.

Lastly, the variable DIMPEE, indicating whether respondents regard energy efficiency as important for their household, is negative. This indicates that they are less likely to make the switch from fixed price to one of the other pricing alternatives. The odds ratio indicates that those who regard energy efficiency are about 45% less likely to make the switch than those who do not regard energy efficiency as important to their household.