Transcript PROJEKT II

Advanced statistics for
master students
Loglinear models II
The best model selection and
models for ordinal variables
3 procedures in SPSS:
1)Loglinear (today and next lecture models with ordinal
variables)
2)Model selection (today)
3)Logit (not included)
Ordinal Loglinear Models
Literature:
Agresti (2002), Wiley; Simonof (2003), Springer;Ishii-Kuntz
(1994), Sage
Model selection procedure
-try to find „the best“hierarchical model
-logic: based on chi-squre tests which compare LR criteria for 2
nested models
-approach: Start with saturated model and through backward go
to the best model (quite opposite strategy can be applied - from
model of independence forward method, sometimes not
reccomended in literature)
-all variables are treated as nominal
Model selection
-2 tests
1) Test that k-way interaction are all zero
2) Test, that k-way and higher interactions are all zero
Model selection procedure in SPSS:
1. Saturated model estimates
2. 2 tests (see above)
3. Proposal for removing nonsignificant the highest order
interactions and computations of new model estimate
4. Again step 2 and 3 (finish-the best model)
5. Computation of parameters of the best model
Model selection
Limits of procedure
1) Only hierarchical models
2) Based on LR tests only, not including principle of parsimony
(see below AIC a BIC etc.)
3) Only models for nominal variables
BUT: For most analytical tasks it can be usefull. The procedure
is very quick. For the first insight into your data this
procedure can be reccomended.
Ordinal Loglinear Models
- One or more variables is treated as ordinal
- We save number of parameters, higher degrees of freedom
(e.g. instead of parameters for every row, only parameter for one
variable can be used, the same can be applied for interactions)
- There are many models in literature, this lecture only two and
three varibles models
-SPSS is limited with the work with ordinal models
Ordinal Loglinear Models
- Row and column effect model – one variable ordinal, one
nominal
- Row effect model – row variable is nominal and column
variable is ordinal, interactions are created by values of column
variable instead of columns
(Example table 3x3: for two nominal variables 4 interaction
parameters, for row effect model only 2)
- Uniform association- two ordinal variables, interaction is
composed by multiplying values of these variables
(Example table 3x3: for two nominal variables 4 interaction
parameters, for row effect model only 1)
Ordinal Loglinear Models
Formulas, equations
- Row and column effect model
- Uniform association
Interpretation of parameters and odds in models
- Row and column effect model
- Uniform association
Model for three variables
Model of independence
Model of constant fluidity, partial asscociation
saturated model
Ordinal Loglinear Models
„The best model!
- Tests for LR criterias
Goodman, AIC BIC criteria
Goodman index G = G2/df,
where G2 is LR criteria (overall test of fit)
df-degrees of freedom
Akaike information criteria AIC = G2 + 2p,
Where p is number of parameters in model
Ordinal Loglinear Models
Goodman, AIC, BIC – continue:
Bayes Schwartz information criteria
BIC = G2-df (ln n),
Where n is number of respondents
The lower the better –logic of all criterias
Problem – different criteria favour different models
Note: These criteria can be used in many statistical techniquesregression analysis, multilevel models, SEM, etc.
Ordinal Loglinear Models
The best model selection – other methods
- Residuals – tests
- Residuals – charts
- Principle of parsimony
Ordinal Loglinear Models summary
Reccomendation for model selection (Ishii-Kuntz 94:53-4)
1)
2)
3)
4)
Prefer model with lower number of parameters (parsimony).
Prefer model with simpler interpretation.
Prefer model with all parameters statistical significant.
Higher Sig. for overall test is good but too big Sig. can be sign of
model icludes too much parameters.
5) For ordinal variables is reccomended to start with models for
nominal data and then use appropriate model with ordinal varibles.
6) The most important rule is to follow the theory and use model proposed
in literature.
Do not apply (or try) all possible models (data driven analysis) but have
some hypothesis in advance about model and test this hypothesis
(theory driven analysis) – (Petr S. 12.4. slide 12)
HW
1) Try to use general loglinear model procedure and find
appropriate model for at lest 3 variables. Interpret results and
tests.
1) Try to find the best model with Model selection on your data
2) Try to use ordinal modelon your data and interpret results.
Compare ordinal model and best hierarchical model (degrees of
freedom, LR, criterias etc.)