The Marketing Book 5th Edition

212 The Marketing Book

 This distribution can be modelled using a linear
equation once it has been transformed.
 The model-building approach of the logistic
regression provides much more detailed
analysis of data than can be obtained using a
t-test, ANOVA, Mann–Whitney or
Kruskal–Wallis.
 The linear component of the model is the
same as that used for the OLS regression.

Log-linear analysis

GLMs can also be used to model categorical
data (i.e. data in the form of contingency
tables). The traditional method of analysing
such data is to interpret bar charts and to use
the chi-square statistic as part of the cross-
tabs procedure. These methods have severe
limitations as they can only deal with two
variables and cannot model the data to pro-
vide predictions. The same considerations
apply to contingency table data as applied to
OLS regression regarding the problems of
interaction variables (e.g. wages, education
and gender).
A log-linear analysis enables much more
information to be obtained from the data and
also enables statistics to assess the overall fit of
the model. As the log-linear name suggests, it is
a technique which makes use of the linear
model and a transformation involving the
natural log. Similar to OLS and logistic regres-
sion, the form of model is a linear
combination:

ln(cell count) = + 1 X 1 + 2 X 2 + 3 X 3

+kXk

The form of the log-linear model is very
similar to the previous models discussed – the
only difference is that we are now modelling
cell counts. In effect, all of the terms in the
model have been moved to the right-hand side
of the equation. Parameters from the model are
similar to the other models, but are interpreted
slightly differently.

Conclusions

 The log-linear model is very similar to the

OLS and logistic regression models.

 All of the advantages of OLS regression, such

as being able to compute model fits, make

predictions and investigate complex

interactions, also apply to log-linear.

 It enables analysis of multi-category,

multi-group data – something not possible

using chi-square.

Discriminant analysis

Like regression analysis, discriminant analysis

(DA) uses a linear equation to predict the

dependent variable (say, sales). However, while

in regression analysis the parameters (coeffi-

cients) are used to minimize the sum of squares,

in discriminant analysis the parameters are

selected in such a way as to maximize the ratio:

Variance between group means

Variance within groups

Discriminant analysis is used in marketing

for predicting brand loyalty and buying or

attempting to predict consumer behaviour in

general; this classification method can be used

when the data (the independent variables) are

interval scales.

Automatic interaction detection

(AID)

The regression analysis mentioned above

attempts to identify association between the

dependent and the independent variables, one

at a time. In addition, the assumption is that the

data are measured on interval scales. In many

other marketing research situations we need a

method able to handle nominal orordinal data

and to identify allthe significant relationships

between the dependent and the independent

variables. Automatic interaction detection

(AID) is a computer-based method for inter-

actively selecting the independent variables in