Description Usage Arguments Details Value Input Data Note Author(s) See Also Examples

Function to fit a loglinear Bradley-Terry for paired comparisons allowing subject covariates and undecided response categories.

1 2 | ```
llbtPC.fit(obj, nitems, formel = ~1, elim = ~1, resptype = "paircomp",
obj.names = NULL, undec = TRUE)
``` |

`obj` |
either a dataframe or the path/name of the datafile to be read. |

`nitems` |
the number of compared objects, not the number of comparisons |

`formel` |
the formula for subject covariates to fit different preference scales for the objects (see below). |

`elim` |
the formula for the subject covariates that specify the table to be analysed. If omitted and |

`resptype` |
is |

`obj.names` |
character vector with names for objects. |

`undec` |
for paired comparisons with a undecided/neutral category, a common parameter will be estimated if |

Models including categorical subject covariates can be fitted using the `formel`

and `elim`

arguments.
`formel`

specifies the actual model to be fitted.
For instance, if specified as `formel = ~SEX`

different preference scale for the objects will be estimated for males and females.
For two or more covariates, the operators `+`

or `*`

can be used to model main or interaction effects, respectively.
The operator `:`

is not allowed.
See also `formula`

.

The specification for `elim`

follows the same rules as for `formel`

.
However, `elim`

specifies the basic contingency table to be set up but does not specify any covariates to be fitted.
This is done using `formel`

.
If, e.g., `elim = ~SEX`

but `formel = ~1`

, then the table is set up as if `SEX`

would be fitted but only one global preference scale is computed.
This feature allows for the successive fitting of nested models to enable the use of deviance differences for model selection (see example below).

`llbtPC.fit`

returns an object of class `llbtMod`

.
This object is basically a `gnm`

object with an additional element `envList`

.
This is a list with further details like the subject covariates design structure `covdesmat`

, the model specification (`formel`

and `elim`

), the object names (`obj.names`

), the number of items (`nobj`

) and comparisons (`ncomp`

), etc.

The function `llbt.worth`

can be used to produce a matrix of estimated worth parameters.

The responses have to be coded as 0/1 for paired comparisons without undecided category (0 means first object in a comparison preferred) or 0/1/2 for paired comparisons with an undecided category (where 1 is the undecided category). Optional subject covariates have to be specified such that the categories are represented by consecutive integers starting with 1. Rows with missing values for subject covariates are removed from the data and a message is printed. The leftmost columns in the data must be the responses to the paired comparisons (where the mandatory order of comparisons is (12) (13) (23) (14) (24) (34) (15) (25) etc.), optionally followed by columns for categorical subject covariates.

The data specified via `obj`

are supplied using either a data frame or a datafile in which case `obj`

is a path/filename.
The input data file if specified must be a plain text file with variable names in the first row as readable via the command `read.table(datafilename, header = TRUE)`

.

For an example see `cemspc`

.

The function `llbtPC.fit`

is a wrapper function for `gnm`

and was designed to facilitate fitting of LLBTs with subject covariates and undecided categories.
More specialised setups (e.g., object-specific covariates) can be obtained using `llbt.design`

and then calling `gnm`

(or `glm`

) directly (see Examples for `llbt.design`

).

Reinhold Hatzinger

1 2 3 4 5 6 | ```
# cems universities example
res0 <- llbtPC.fit(cemspc, nitems = 6, formel = ~1, elim = ~ENG, undec = TRUE)
res1 <- llbtPC.fit(cemspc, nitems = 6, formel = ~ENG, elim = ~ENG, undec = TRUE)
anova(res1, res0)
llbt.worth(res1)
``` |

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