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Expertise We have present all necessary statistical model to treat categorical data problems whit their application fields. Now we can see more models details. Although all treat models belong only one models family, the substantial differences from one to another are diverse. L o g i s t i c r e g r e s s i o n v s . L o g l i n e a r m o d e l s
The log-linear model defer from logistic model for that causes: 1.The dependent variable is categorical and not continuous 2.It useful to describe the relation between response variable in explanatory variable functions. 3.The variables waiting distribution is a Poisson, and not binomial 4.The function is log and not logit 5.The previsions are cells esteems of a contingency table , not a logit of Y. L o g l i n e a r m o d e l s v s . L i n e a r - l o g i t m o d e l s
The linear-logit model is a loglinear model extension and bring out the same result. In this case the model differ in the treat variable. In fact logit model can treat a independent continuous or categorical variable set respect a dependent categorical or response variable. The log-linear model can treat all variables in the same way, it don't difference independent or dependent variables. M o r e d e t a i l s a b o u t l o g - l i n e a r m o d e l s :
The base strategy in the use of log-linear models is start from the data and mould the model from the contingency table cells
frequency, they express the categorical variables. It construct a set of "useful" model on esteemed frequency and then we mould it
until to obtain the "best-fit".
This is the model:
Ln(F ij ) = m + l i A + l j B + l k C + l ij AB + l ik AC + l jk BC + l ijk ABC
Where l i are the system parameters. They express the dependence from a variable to another.
The problem hierarchy analysis allow to construct more than a model to a single problem. In fact it put in a parameter or in more
parameter the "zero" value. Then we can choose a formulate model with the 'good adaptable, parsimony, and substantial meaning'
principle. We can explain step to step the way to discover the exact model :
1.Inquiry: a study preliminary phase is an inquiry to pinpoint the models.
2.Fitting: we can pinpoint problem and model, and then we can calculate and tabulate the waiting frequency (Fij):
a)For 2*2 tables, we can use the under formula to value the direct esteem for no saturate model: (total-columns)*(total-rows)/total-absolute. b)For big tables, we can use an minimal errors interactive algorithms to generate the waiting frequency(Deming-Stephan algorithmic). This algorithmic can do maximum likelihood waiting esteems to a hierarchy model. 3.Parameters esteem: the value obtain from waiting frequency had put in the formulas opportune and it product the parameter
esteem, that represent the effects on the variables and its interactions.
4.Verification: with the complete models, we can verify what is the best esteemed (goodness-of-fit). This operation can be do to
compare the observe values whit esteem values of the waiting frequency.
As statistic operator we use the 'maximum likelihood' c 2 Pearson rapport:
c 2 =2* S f ij *ln(f ij /F ij );
where fij= esteemed values , Fij= observed values.

Source: http://www.scienzeregionali.it/geomemo/Inglese/Modelli/DataAnalysis/Categorical/PDF/03-Categorical.pdf

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