SampleStatistics: SampleStatistics

Description

Gives sample values, standard errors and z-scores of one or more coefficients. SampleStatistics(dat,coeff) gives exactly the same output as ModelStatistics(dat,dat,"SaturatedModel",coeff).

Usage

SampleStatistics(dat, coeff, CoefficientDimensions = "Automatic", 
 Labels = "Automatic", ShowCoefficients = TRUE, ParameterCoding = "Effect", 
 ShowParameters = FALSE, ShowCorrelations = FALSE, Title = "", ShowSummary = TRUE)

Value

A subset of the output of MarginalModelFit.

Arguments

dat: observed data as a list of frequencies or as a data frame
coeff: list of coefficients, can be obtained using SpecifyCoefficient, or a predefined function such as "log"
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
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
ShowSummary: Show summary on the screen

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

if (FALSE) {
data(BodySatisfaction)

## Table 2.6 in Bergsma, Croon and Hagenaars (2009). Loglinear parameters for marginal table IS
## We provide two to obtain the parameters

dat   <- BodySatisfaction[,2:8]        # omit first column corresponding to gender

# matrix producing 1-way marginals, ie the 7x5 table IS
at75 <- MarginalMatrix(var = c(1, 2, 3, 4, 5, 6, 7), 
 marg = list(c(1),c(2),c(3), c(4),c(5),c(6),c(7)), dim = c(5, 5, 5, 5, 5, 5, 5))

# First method: the "coefficients" are the log-probabilities, from which all the 
# (loglinear) parameters are calculated
stats <- SampleStatistics(dat = dat, coeff = list("log",at75), CoefficientDimensions = c(7, 5),
 Labels = c("I", "S"), ShowCoefficients = FALSE, ShowParameters = TRUE)

# Second method: the "coefficients" are explicitly specified as being the 
# (highest-order) loglinear parameters
loglinpar75 <- SpecifyCoefficient("LoglinearParameters", c(7, 5))
stats <- SampleStatistics(dat = dat, coeff = list(loglinpar75, at75), 
 CoefficientDimensions = c(7,5), Labels = c("I","S"))
}

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