SampleStatistics | R Documentation |

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)`

.

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

`dat` |
observed data as a list of frequencies or as a data frame |

`coeff` |
list of coefficients, can be obtained using |

`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 |

`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 |

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`

).

A subset of the output of `MarginalModelFit`

.

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

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`

```
## 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)
```

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