ModelStatistics: ModelStatistics

Description

If fitted frequencies under a model have been calculated, this procedure can be used to give sample values, fitted values, estimated standard errors, z-scores and adjusted residuals of one or more coefficients.

Usage

ModelStatistics(dat, fitfreq, model, coeff, CoefficientDimensions = "Automatic",
    Labels = "Automatic", Method = "ML", ShowCoefficients = TRUE, ShowParameters = FALSE, 
    ParameterCoding = "Effect", ShowCorrelations = FALSE, Title = "")

Value

A subset of the output of MarginalModelFit.

Arguments

dat: observed data as a list of frequencies or as a data frame
fitfreq: vector of fitted frequencies for each cell of full table (including latent variables, if any)
model: list specified eg as list(bt,coeff,at)
coeff: list of coefficients, can be obtained using SpecifyCoefficient
CoefficientDimensions: numeric vector of dimensions of the table in which the coefficient vector is to be arranged
Labels: list of characters or numbers indicating labels for dimensions of table in which the coefficient vector is to be arranged
ShowCoefficients: boolean, indicating whether or not the coefficients are to be displayed
ShowParameters: boolean, indicating whether or not the parameters (computed from the coefficients) are to be displayed
Method: character, choice of "ML" for maximum likelihood or "GSK" for the GSK method
ParameterCoding: Coding to be used for parameters, choice of "Effect", "Dummy" and "Polynomial"
ShowCorrelations: boolean, indicating whether or not to show the correlation matrix for the estimated coefficients
Title: title of computation to appear at top of screen output

Author

W. P. Bergsma w.p.bergsma@lse.ac.uk

Details

The data can be a data frame or vector of frequencies. MarginalModelFit converts a data frame dat using c(t(ftable(dat))).

For ParameterCoding, the default for "Dummy" is that the first cell in the table is the reference cell. Cell \((i,j,k,...)\) can be made reference cell using list("Dummy",c(i,j,k,...)). For "Polynomial" the default is to use centralized scores based on equidistant (distance 1) linear scores, for example, if for \(i=1,2,3,4\), \(\mu_i=\alpha+q_i\beta+r_i\gamma+s_i\delta\) where \(\beta\) is a quadratic, \(\gamma\) a cubic and \(\delta\) a quartic effect, then \(q_i\) takes the values \((-1.5,-.5,.5,1.5)\), \(r_i\) takes the values \((1,-1,-1,1)\) (centralized squares of the \(q_i\)), and \(s_i\) takes the values \((-3.375,-.125,.125,3.375)\) (cubes of the \(q_i\)).

References

Bergsma, W. P. (1997). Marginal models for categorical data. Tilburg, The Netherlands: Tilburg University Press. http://stats.lse.ac.uk/bergsma/pdf/bergsma_phdthesis.pdf

Bergsma, W. P., Croon, M. A., & Hagenaars, J. A. P. (2009). Marginal models for dependent, clustered, and longitudunal categorical data. Berlin: Springer.

Examples

Run this code


# Below an example where ModelStatistics can be used to get output for coefficients 
# not given by MarginalModelFit 

# Marginal homogeneity (MH) in a 3x3 table AB
# Note that MH is equivalent to independence in the 2x3 table of marginals IR, in which the 
# row with I=1 gives the A marginal, and the row with I=2 gives the B marginal 
n <- 1 : 9
at <- MarginalMatrix(c("A", "B"), list(c("A"), c("B")), c(3,3))
bt <- ConstraintMatrix(c("I", "R"), list(c("I"), c("R")), c(2,3))
model <- list( bt, "log", at)

#The "coefficients" for the model are the log marginal probabilities for table IR
fit <- MarginalModelFit(dat = n, model = model, 
 CoefficientDimensions = c(2, 3), Labels = c("I", "R"))

#to get output for the marginal probabilities, ModelStatistics can be used as follows
spec <-  SpecifyCoefficient("ConditionalProbabilities",list(c("I","R"),c("I"),c(2,3)))
coeff <- list(spec, at)
stats <- ModelStatistics(dat = n, fitfreq = fit$FittedFrequencies, 
 model = model, coeff = coeff, CoefficientDimensions = c(2, 3),
 Labels = c("I", "R"))

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