ModelStatistics | R Documentation |

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.

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

`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 |

`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 |

`Method` |
character, choice of "ML" for maximum likelihood or "GSK" for the GSK method |

`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 |

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`

```
# 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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