Predicting actual cancellation

Logistic regression is often used in the health sciences and epidemiological studies whereby the dependent variable has two categories e.g. disease/no disease, survival/death. Binary logistic regression was used to assess the influence that the independent variables might have over actual cancellation of membership. This is due to the fact that actual cancellation is a dichotomous variable; after twelve months of participants completing the questionnaire, they had either cancelled their membership or they had retained it. As with all inferential statistical analyses, there are certain requirements regarding the appropriate use of logistic regression.

7.4.2.1 Logistic regression requirements

Whilst logistic regression is non-parametric and therefore does not require the assumptions of normality to be met, the main consideration is whether there are enough events per variable (EPV). According to Peduzzi, Concato, Kemper, Holford and Feinstein (1996), there should be a minimum of ten ‘events’, for the least frequently occurring outcome, per independent variable included in the model to avoid any risk of underestimation or overestimated variances. Standalone, within the dataset there are 81 events (members) who actually cancelled their membership (the least frequently occurring outcome), and 635 events who retained their membership. Thus, with 81 events being the least frequently occurring outcome, based on this rule of 10 events per variable rule this would suggest that only 8 independent variables are included in any model tested at any one time.

However, the number of events will also be determined by the response rate for each variable also being included in the model. For instance, whilst there may have initially been 81 participants who cancelled their membership, when this group was also cross-tabulated with other variables, the rule of 10 EPV is not always met, as the way in which actual

cancellation combines with other variables in the analysis which may have missing data will naturally reduce the EPV. It has also been argued, however, that this rule can be relaxed. For instance, Vittinghoff and McCulloch (2007) conducted two simulation studies to test the influence of EPV, finding that the results obtained between five and nine EPV were comparable to those found with 10 EPV.

However, to optimize the EPV the first step taken was to conduct a series of individual analyses, analysing each independent variable’s efficacy in predicting actual cancellation. Whilst conducting individual analyses increase the amount of error, this helped to ensure there were always at least 10 events in actual cancellation outcome group.

7.4.2.2 Reporting and interpreting logistic regression

Whilst logistic regression is generally becoming more popular as a statistical technique (Tabachnick & Fidell, 2007), in a search of 12 consumer-related journals, only 77 articles were found which had published the use of logistic regression (Akinci, Kaynak, Atilgan & Aksoy, 2007). This is surprising considering that consumer decision-making is often based on certain discrete choices, such as whether or not to cancel fitness club membership. Due to its rarity in the consumer literature, it is perhaps necessary to provide guidance on how logistic regression analysis results should be reported and interpreted. Field (2005) states that there is little consensus in exactly which coefficients to report, due to the rarity of logistic regression in social science, as opposed to in other sciences premised on epidemiological studies, predicting rare ‘events’ within a large-scale sample whereby the outcome group will often be very unbalanced. However, Field suggests reporting the beta weights (B and exp B), as well as the standard error and alpha levels which denote the significance of the beta coefficient after conducting logistic regression analyses. The beta values in logistic regression relate to those used in linear regression, both indicating the impact of a unit change in the predictor variable on the outcome variable.

However, the main difference is that in linear regression, B represents a change in the value of the outcome variable; whereas in logistic regression B represents the change in the odds that a case will be categorised into one of two groups. However, there are two beta coefficients in logistic regression; B and Exp B. ‘Exponential beta weights’ (Exp B) are related to B, but whereas B in logistic regression represent the effect of a unit increase to the likelihood, exp B is simply an expression of this change as an increase in odds.

If there was no effect of the predictor variable on the categorisation of a case into the outcome group, B would be 0 (zero effect), and the exp B would be 1 which represents a 50/50 (equals 1), probability that this categorisation into a certain group would occur, no better than tossing a coin. Thus, the closer the exp B value to 1, the smaller effect size. For instance, an exp B value of, say, 1.5 represents a 50% increase in the probability that the categorisation will occur; 0.5 representing a 50% decrease.

The results of the logistic regression analyses conducted to ascertain the predictors of actual cancellation are now discussed.

7.4.2.3 Preliminary binary logistic regression analyses

All variables were firstly tested individually to ascertain whether they could predict actual cancellation. However, only three variables were found to predict actual cancellation; state anxiety (staff), state anxiety (members) and intention to cancel. These three results are shown below in Table 7.4.

Table 7.4 Binary logistic regression results of actual cancellation predictors

B S.E. Wald Exp(B) Model chi-

square Intention to cancel -.43 .08 28.18 .65** 25.74*** State anxiety- staff -.31 .09 11.60 .73** 10.86** State anxiety- members -.26 .09 8.90 .77** 8.42** Note: ** p< .01. *** p< .001.

Overall, across the whole dataset, a unit increase in intention to cancel (exp b=.65, B= - .43, SE= .08., p=<.01) state anxiety (staff) (exp b= .73, B= -.31, SE=.09, p=<.01) and state anxiety (members) (exp b= .77, B= -.26, SE=.09, p=<.01) were each found to decrease the likelihood of members being in the category of those who retained their membership. After establishing the predictive efficacy of these three predictors at an individual level, it was then necessary to model them together. However, when these three predictors were included in the same model, state anxiety (members) was no longer significant. As such, the analysis was re-run including just state anxiety (staff), and intention to cancel, with the results detailed below.

7.4.2.4 State anxiety (staff) and intention to cancel

State anxiety (staff) and intention to cancel were the two predictors in the final binary logistic model predicting actual cancellation. As shown in Table 7.5, across the whole dataset, when modelled together a unit increase in intention to cancel (exp b=. 67, B= -.40 SE= .08, p=<.001) and a unit increase in their state anxiety (exp b= .77, B= -.27, SE=.10, p=<.01) were together found to decrease the likelihood of members being in the category of those who retained their membership.

Table 7.5 State anxiety (staff) and intention to cancel predicting actual cancellation

B S.E. Wald Exp(B) Model chi-

square

Full dataset (n=642)

State anxiety- staff -0.27 0.10 7.93 0.77** 33.20*** Intention to cancel -0.40 0.08 24.53 0.67***

Constant 3.55 0.32 122.95 34.89***

First-half (n=333)

State anxiety- staff -0.28 0.14 4.15 0.76* 18.95*** Intention to cancel -0.45 0.12 14.34 0.64***

Constant 3.92 0.49 63.32 50.211***

Second-half (n=309)

State anxiety- staff -0.29 0.14 4.51 0.75* 15.52*** Intention to cancel -0.37 0.11 10.68 0.69**

Constant 3.30 0.43 59.27 27.18*** Note: * p< .05. ** p< .01. *** p< .001.

These were verified on the first half of the dataset; (intention to cancel, exp b=. 64, B= -.45, SE= .12, p=<.001; state anxiety-staff, exp b=. 76, B= -.28, SE= .14, p=<.05) and also on the second half of the dataset (intention to cancel, exp b=. 69, B= -.37, SE= .11, p=<.01; state anxiety-staff, exp b=. 75, B= -.29, SE= .11, p=<.05).

This analysis helped to address Objective 2; to assess the efficacy that the potentially predictive variables have over predicting the cancellation (actual and intentional) of current fitness club members. It was indicated that intention to cancel and state anxiety (staff) were predictive of actual cancellation. Thus, Objective 3; to assess the efficacy that intentional cancellation has over predicting actual cancellation of current fitness club members had also been addressed in this analysis.