5. Results
5.2 Study 2
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significantly which indicated a good fit (2 (168) = 176.89, p < .10). The performance of the model to correctly classify outcomes was also estimated by examining the value under the Receiver Operating Characteristic (ROC) curve. This returned value was 0.8470 which indicated acceptable
discrimination for the model (Mandrekar, 2010).
The robustness of the model was strengthened by altering two independent variables which could have been constructed differently to see if the results remained similar. The variable type was constructed as continuous variable where the utilitarian dimension was reverse coded. Another possibility would have been to create a binary variable equal to 0 if the utilitarian scale was larger and 1 if the hedonic scale was larger. Model 4 under Appendix VII shows the same regression as model 3 of table 7 but now with the variable type_2 being this binary variable. The main independent variable device lost some significance but the same conclusions with respect to hypothesis 1 and 2 could still be drawn. Interestingly, the new variable type_2 had no significant direct effect on cross-channel free riding intentions ( = .69, p > .10), while in model 3 hedonic products significantly increased cross-channel free riding intentions ( = .93, p < .01). The pseudo R2 dropped from 32% to 27%, but the model is still highly significant (2 (13) = 63.71, p < .01).
Model 5 shows the specification where the variable for the product price is not split in 10 equally sized bins, but the continuous value in euros is used. The same relations with regard to the hypotheses are drawn compared to model 3, indicating that the main model is robust to different constructions of the variable price. Model 6 combines the two differently created variables in one model and again the same conclusions are drawn with respect to the hypotheses but the pseudo R2 drops to 24%. This confirms that the main model used in table 7 is the most accurate and also robust against different variations of the same variable.
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similar across groups, which was confirmed (F (7, 158) = 1.7, p > .10). This was especially important because this variable was significant in most models in study 1.
5.2.2 Data examination
Some variables needed to be recoded to fit the analysis. All measures for free riding and customer loyalty were asked separately for each condition and therefore new variables were created to generate one homogenous variable for all conditions. Afterwards, the univariate normality of the variables was checked by looking at the skewness and kurtosis. The constructed variables for customer loyalty and attitude showed no signs of non-normality as both kurtosis and skewness are lower than |1|, presented under Appendix VIII. The variable for cross-channel free riding consists of two measures and the item
‘cross intentions’ returned a kurtosis lower than -1. However, since the value -1.033 is extremely close to -1 and Westfall & Henning (2013) argued that a value of -2 is allowed in most instances, no transformations were made. The experiment specific variables are device, type and price. Each condition was assigned a binary value for each variable accordingly to the condition. For example, the purchase of an expensive utilitarian product on a fixed device in condition 6, received a 1 for device, a 0 for type and a 1 for price. All other variables are coded similarly as in study 1.
5.2.3 Reflective constructs
The constructed variables for study 2 were checked on reliability. The first measure which calculates the main dependent variable freeriding appeared to be reliable ( = .87). Because the measure consists of only two items it cannot be checked for robustness when an item would be dropped. The variable loyalty is also reliable ( = .94) and robust since the Cronbach’s alpha would remain above .91 if any of the items is removed. The last variable that is checked is the control variable attitude which is reliable ( = .88) and robust against removed items ( > .82). Furthermore, the variables were checked on convergent and divergent validity with the use of a correlation matrix, shown under appendix IX. The variables passed both tests as for the convergent validity all items have a correlation coefficient with the score of their own dimension greater than 0.4. For the divergent validity test all items have a correlation coefficient with the score of their own dimension greater than those computed with other scores. After the reliability was confirmed, the composite measures were generated. Again, the summated scales method with equal weights was used.
5.2.4 Descriptive statistics
Table 8 presents the correlation matrix with Pearson correlation coefficients of the relevant variables with their mean and standard deviation. Compared to study 1, it can be observed that a similar amount of people had cross-channel free riding intentions (M = 3.21 = 64.2% out of 5). Furthermore, the variable loyalty shows similar characteristics as study 1 (M = 3.63), while the control variables
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attitude, age, gender and education also display no large deviations. This provides important evidence to the validity of the data collection process, which seems to have occurred random and correctly.
Only the largest deviations with respect to study 1 in terms of correlation will be discussed. In study 2, the main dependent and independent are significantly correlated at the 5% level (r = .42, p <
.05) which already highlights the first evidence for the relation between the two variables to exist in the experiment. Interestingly, freeriding is significantly negatively correlated with attitude (r = -.25, p
< .05), while it is expected that a more positive attitude towards online searching would be correlated with higher cross-channel free riding intentions. A negative correlation of attitude with age can be observed (r = -.25, p < .05), which is somewhat expected as young people are more proficient using devices for search purposes. Other important variables all show similar correlations compared to study 1 and therefore the results obtained in both studies should have higher external validity.
Table 8. Pairwise Pearson correlation matrix of the relevant variables of study 2.
Variable Mean SD Freeriding Device Loyalty Type Price Attitude Age Gender Education Freeriding 3.21 1.19 (0.87)
Device .48 .50 .42** --
Loyalty 3.50 .99 -.30** -.01 (0.94)
Type .50 .50 .26** .00 -.23** --
Price .49 .50 .22** .01 .04 .02 --
Attitude 3.75 .83 -.25** -.17* .21** -.09 -.02 (0.88)
Age 2.13 1.29 .03 .15 -.07 -.01 .04 -.25** --
Gender .52 .50 .12 -.02 .13 -.06 -.02 .05 -.13 --
Education 3.25 1.23 .11 .03 -.17* .03 -.03 .02 -.09 .08 --
** p < .01, * p < .05
N = 166 and Cronbach’s alphas in parentheses and bold.
5.2.5 Preliminary results
The mean values of cross-channel free riding intentions were compared across the two different type of devices similarly as study 1. Participants who had to use a fixed device showed higher intentions to engage in cross-channel free riding (M = 3.73) compared to the mobile device (M = 2.73). Figure 3 presents the difference in this mean value visually and it can be observed that it follows an extremely similar pattern as figure 2 from study 1. The dependent variable freeriding is continuous and therefore a one-way ANOVA was used to calculate if this mean difference is significantly different from 0.
However, after performing the ANOVA and examining the assumptions, the homogeneity of
variances assumption was violated (Levene = 12.61, p < .01). Therefore, a Welch test was conducted instead. This test confirmed there is a significant difference in the mean values between the two
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devices (W = 36.05, p < .01). Consequently, increasingly more evidence in favour of hypothesis 1 was collected.
Figure 3. Difference in means of cross-channel free riding intentions between devices in study 2.
5.2.6 Regression analysis
A regression analysis was conducted to review all hypotheses simultaneously. In this study, the dependent variable freeriding was measured on a continuous scale and therefore OLS regressions could be used. Table 9 presents the regression output of the different models. Model 1 shows the regression of the variable freeriding on the control variables. The model is statistically significant (F(4, 161) = 3.68, p < .01) and the R2 is equal to .09 which means that model 1 is able to explain 9%
of the proportion of the total variation in freeriding. The coefficient for attitude is significantly negative ( = -.37, p < .01), which is expected based on the negative correlation between the variables observed in table 8 but still is a surprising result.
In model 2 the main independent variable device and the moderators were included. After the inclusion of these variables, the model’s R2 increased to 40%, which is a significant increase over model 1 (F(4, 157) = 20.78, p < .01). In the model, device has a significantly positive relation to freeriding ( = .97, p < .01), which provides more evidence to support hypothesis 1. Furthermore, the direct effects of the moderator variables on freeriding have the same direction as in study 1 and are all three highly significant (p < .01). It highlights that these variables behave similarly and as expected in both studies which adds to the robustness of the research. Interestingly, the coefficient for gender returned significantly positive ( = .42, p < .01), which indicates that on average females have higher intentions to engage in cross-channel free riding in this setting. This does not pose any problems to the credibility of the experiment, because table 8 shows no significant correlation between gender and freeriding and randomization was done successfully across gender.
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In model 3, the interaction terms of the moderator variables with the main independent variable freeriding were added. The model’s R2 increased to 41%, but this is not a significant increase from model 2 (F(3, 154) = .56, p > .10). The continuous independent variable loyalty was first
standardized to avoid problems with multicollinearity. All three interaction terms are insignificant and do not provide evidence for hypotheses 2, 3 or 4. While on average the interaction between device and loyalty produced an expected negative coefficient, the other interactions of device on type and device on price do not show the expected positive relation. The main independent variable device remains statistically significant ( = 1.15, p < .01), while the direct effect of loyalty on freeriding loses its significance ( = -.23, p > .10).
Table 9. Hierarchical OLS regression of main dependent variable freeriding.
Dep. Variable:
Freeriding (1) (2) (3)
Device .97*** 1.15***
(6.51) (4.39)
Device * Loyalty -.15
(-.84)
Device * Type -.12
(-.39)
Device * Price -.24
(-.81)
Loyalty -.31*** -.23
(-3.41) (-1.6)
Type .45*** .50**
(2.9) (2.2)
Price .54*** .66***
(3.7) (2.89)
Attitude -.37*** -.18* -.18*
(-3.09) (-1.82) (-1.8)
Age -.01 -.06 -.06
(-.12) (-.96) (-1.04)
Gender .29 .42*** .39***
(1.64) (2.92) (2.77)
Education .10 .04 .03
(1.42) (.59) (.47)
Constant 4.12*** 3.79*** 2.68***
(7.55) (6.15) (5.30)
N 166 166 166
R-squared .09 .40 .41
t-values are in parentheses
*** p < .01, ** p < .05, * p < .10 Loyalty is standardized in model 3
45 5.2.7 Assumptions and robustness checks
Several OLS assumptions needed to be checked for the obtained results to be marked as reliable from a statistical standpoint. Firstly, the assumption of no multicollinearity was checked by calculating the VIF of each variable for all models. The tables under Appendix X show there are no problems relating to multicollinearity as all values are below 5. Next, the homoscedasticity assumption was checked for the main model 3. This was reviewed by first observing a plot of the residuals across the fitted values to see any deviations in variance. The plot is shown under Appendix XI and no large deviations in variance were observed. This was confirmed by a White test of heteroskedasticity which did not reject the null hypothesis of homoscedasticity (2 = 68.10, p > .10). Lastly, the normality of the residuals for model 3 was examined by observing the distribution of the residuals in a kernel density plot and QQ plot, which are listed under Appendix XII. The residuals follow the normal distribution line
reasonably well and with a Shapiro-Wilk W test for normality this normality was confirmed (W = .99, p > .05).
The robustness of the regression analysis was strengthened by replicating the main model with different constructions of the dependent variable freeriding. In the experiment, participants were also asked to their intentions to specifically stay within the firm’s channels and as a result more variations of the variable freeriding could be constructed. In Model 4 under Appendix XIII this scale was utilized to create the variable retention and it was used as dependent variable to see if reversed relations could be observed. The model shows that using a fixed device for search purposes decreases the intentions to stay within the firm’s channels by 1.02 ( = -1.02, p < .01). However, similar to model 3, no evidence was found for the existence of the interaction effects. Additionally, loyalty is significantly positively related to retention ( = .37, p < .05), while price is negatively related ( = -.53, p < .05). There is no statistical evidence for hedonic products to decrease the intentions to not free ride. The R2 of this model is lower compared to model 3, 36% compared to 41%. Therefore, model 4 is less preferred when it comes to explaining the proportion of the variation of the dependent variable.
In model 5, a combination of the dependent variable freeriding and retention was used. The variable is a subtraction of retention from freeriding and subsequently the created variable has a longer possible range [-4, +4], which could provide additional information compared to when the variables are used separately. Model 5 shows largely similar results compared to model 3. The coefficient for device is significantly positive ( = 2.17, p < .01), but again the coefficients of the interactions are not significantly different from 0. Meanwhile, the direct effect of loyalty is significantly negative in this model ( = -.60, p < .05) and hence the R2 is moderately higher compared to model 3 with 43%, which indicates that this model performs better and is therefore actually preferred.
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