# SampleStatistics: SampleStatistics In cmm: Categorical Marginal Models

 SampleStatistics R Documentation

## 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)

### 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

### 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).

### Value

A subset of the output of MarginalModelFit.

### Author(s)

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

### 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.

ModelStatistics, MarginalModelFit

### Examples

## Not run:
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"))

## End(Not run)


cmm documentation built on Aug. 10, 2023, 1:07 a.m.