15 McFadden. The following equations are the formula to get pseudo r-squared
statistics in logistic regression model Tabachnick and Fidell 2006.
Cox and Snell:
Nagelkerke:
McFadden:
LLB : Log-likelihood Final Model LL0 : Log-likelihood Constant Model
Equation 3. Pseudo R-Squared
2.4.2 Significance Tests for The Coefficients
The MLR analysis can be done by using several methods in order to select the important variables for building a model. The popular method is stepwise
method which is a stepwise procedure for selection or deletion of variables from a model based on a statistical algorithm that checks for the importance of variables,
and either includes or excludes them on the basis of a fixed decision rule. The importance of a variable is defined in terms of a measure of the statistical
significance of the coefficient for the variable Hosmer and Lemeshow 2000. There are four terms of stepwise method which provided in SPSS software as
shown in the Table 2. The SPSS Logistic Regression offers forward or backward statistical
regression, either of which can be based on either the likelihood ratio or Wald statistic, with user specified tail probabilities Tabachnick and Fidell 2006. The
likelihood ratio test, G-test, is used to test the significance of the parameters which involved in the model. The formula of likelihood ratio as follows:
16 with hypothesis of test:
H =
β =
β
1
= β
2
= β
3
= … = β
p
= 0 H
1
= at least one βi is not the same as zero.
Furthermore, the Wald test is used to test the significance of parameter β
j
, where j = 1,2,3, .., p partially. The formula of Wald test:
where β
j
is the coefficient and SE
βj
is its standard error. Wald test denotes a random variable following the standard normal distribution Hosmer and
Lemeshow 2000. Hauck and Donner 1977 in Hosmer and Lemeshow 2000 examined the performance of the Wald test and found that it behaved in an
aberrant manner, often failing to reject the null hypothesis when the coefficient was significant. They recommended that the likelihood ratio test be used.
Table 2. Stepwise Method for Building MLR Model
Stepwise Terms Description
Forward entry This method begins with no stepwise terms in the model. At
each step, the most significant term is added to the model until none of the stepwise terms left out of the model would have a
statistically significant contribution if added to the model.
Backward elimination
This method begins by entering all terms specified on the stepwise list into the model. At each step, the least significant
stepwise term is removed from the model until all of the remaining stepwise terms have a statistically significant
contribution to the model.
Forward stepwise This method begins with the model that would be selected by
the forward entry method. From there, the algorithm alternates between backward elimination on the stepwise terms in the
model and forward entry on the terms left out of the model. This continues until no terms meet the entry or removal criteria.
Backward stepwise This method begins with the model that would be selected by
the backward elimination method. From there, the algorithm alternates between forward entry on the terms left out of the
model and backward elimination on the stepwise terms in the model. This continues until no terms meet the entry or removal
criteria.
Source: SPPS Help Topics
