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21
Multinomial Lo
gistic Regression
Multinomial Logistic Regression Options
Figure 3-6
Multinomial Logistic Regression Options dialog box
You can specify the following options for your Multinomial Logistic Regression:
Dispersion Scale.
Allows you to specify the dispersion scaling value that will be
used to correct the estimate of the parameter covariance matrix.
Deviance
estimates
the scaling value using the deviance function (likelihood-ratio chi-square) statistic.
Pearson
estimates the scaling value using the Pearson chi-square statistic. You can
also specify your own scaling value. It must be a positive numeric value.
Stepwise Options.
These options give you control of the statistical criteria when
stepwise methods are used to build a model. They are ignored unless a stepwise
model is specified in the Model dialog box.
ɸ
Entry Probability.
This is the probability of the likelihood-ratio statistic for variable
entry. The larger the specified probability, the easier it is for a variable to enter
the model. This criterion is ignored unless the forward entry, forward stepwise,
or backward stepwise method is selected.
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22
Chapter 3
ɸ
Removal Probability.
This is the probability of the likelihood-ratio statistic for
variable removal. The largerthe specified probability, the easier it is for a variable
to remain in the model. This criterion is ignored unless the backward elimination,
forward stepwise, or backward stepwise method is selected.
ɸ
Minimum Stepped Effect in Model.
When using the backward elimination or
backward stepwise methods, this specifies the minimum number of terms to
include in the model. The intercept is not counted as a model term.
ɸ
Maximum Stepped Effect in Model.
When using the forward entry or forward
stepwise methods, this specifies the maximum number of terms to include in the
model. The intercept is not counted as a model term.
ɸ
Hierarchically constrain entry and removal of terms.
This option allows you to
choose whether to place restrictions on the inclusion of model terms. Hierarchy
requires that for any term to be included, all lower order terms that are a part of
the term to be included must be in the model first. For example, if the hierarchy
requirement is in effect, the factorsMaritalstatusandGendermust both be in the
model before theMaritalStatus*Genderinteraction can be added. The three
radio button options determine the role of covariates in determining hierarchy.
Multinomial Logistic Regression Save
Figure 3-7
Multinomial Logistic Regression Save dialog box
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23
Multinomial Lo
gistic Regression
The Save dialog box allows you to save variables to the working file and export
model information to an external file.
Saved variables.
ɸ
Estimated response probabilities.
These are the estimated probabilities of
classifying a factor/covariate pattern into the response categories. There are as
many estimated probabilities as there are categories of the response variable; up
to 25 will be saved.
ɸ
Predicted category.
This is the response category with the largest expected
probability for a factor/covariate pattern.
ɸ
Predicted category probabilities.
This is the maximum of the estimated response
probabilities.
ɸ
Actual category probability.
This is the estimated probability of classifying a
factor/covariate pattern into the observed category.
Export model information to XML file.
Parameter estimates and (optionally) their
covariances are exported to the specified file.SmartScore and future releases of
WhatIf?willbeabletousethisfile.
The SPSS command language also allows you to:
ɸ
Specify the reference category of the dependent variable.
ɸ
Include cases with user-missing values.
ɸ
Customize hypothesis tests by specifying null hypotheses as linear combinations
of parameters.
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Chapter
4
Probit Analy
sis
This procedure measures the relationship between the strength of a stimulus and the
proportion
of cases exhibiting a certain response to the stimulus. It is useful for
situations where you have a dichotomous output that is thought to be influenced or
caused by levels of some independent variable(s) and is particularly well suited to
experimen
tal data. This procedure will allow you to estimate the strength of a stimulus
required to induce a certain proportion of responses, such as the median effective dose.
Example.
How effective is a new pesticide at killing ants, and what is an appropriate
concentr
ation to use? You might perform an experiment in which you expose samples
of ants to different concentrations of the pesticide and then record the number of ants
killed and the number of ants exposed. Applying probit analysis to these data, you
can deter
mine the strength of the relationship between concentration and killing, and
you can determine what the appropriate concentration of pesticide would be if you
wanted to be sure to kill, say, 95% of exposed ants.
Statist
ics.
Regression coefficients and standard errors, intercept and standard
error, Pearson goodness-of-fit chi-square, observed and expected frequencies, and
confidence intervals for effective levels of independent variable(s). Plots: transformed
respon
se plots.
This pr
ocedure uses the algorithms proposed and implemented in NPSOL
®
by Gill,
Murray, Saunders & Wright to estimate the model parameters.
Probit
Analysis Data Considerations
Data.
F
or each value of the independent variable (or each combination of values for
multiple independent variables), your response variable should be a count of the
number of cases with those values that show the response of interest, and the total
25
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26
Chapter 4
observed variable should be a count of the total number of cases with those values for
the independent variable. The factor variable should be categorical, coded as integers.
Assumptions.
Observations should be independent. If you have a large number of
values for the independent variables relative to the number of observations, as you
might in an observational study, the chi-square and goodness-of-fit statistics may
not be valid.
Related procedures.
Probit analysis is closely related to logistic regression; in fact, if
you choose the logit transformation, this procedure will essentially compute a logistic
regression. In general, probit analysis is appropriate for designed experiments,
whereas logistic regression is more appropriate for observational studies. The
differences in output reflect these different emphases. The probit analysis procedure
reports estimates of effective values for various rates of response (including median
effective dose), while the logistic regression procedure reports estimates of odds
ratios for independent variables.
Obtaining a Probit Analysis
E
Analyze
Regression
Probit...
27
Probit Analysi
s
Figure 4-1
Probit Analysis dialog box
E
Select a response frequency variable. This variable indicates the number of cases
exhibiting a response to the test stimulus. The values of this variable cannot be
negative.
E
Select a total observed variable. This variable indicates the number of cases to which
the stimulus was applied. The values of this variable cannot be negative and cannot
be less than the values of the response frequency variable for each case.
Optionally, you can select a Factor variable. If you do, click
Define Range
to define
the groups.
E
Select one or more covariate(s). This variable contains the level of the stimulus
applied to each observation. If you want to transform the covariate, select a
transformation from the Transform drop-down list. If no transformation is applied
and there is a control group, then the control group is included in the analysis.
E
Select either the
Probit
or
Logit
model.
ɸ
Probit Model.
Applies the probit transformation (the inverse of the cumulative
standard normal distribution function) to the response proportions.
ɸ
Logit Model.
Applies the logit (log odds) transformation to the response
proportions.