eba.order {eba} | R Documentation |

Fits a (multi-attribute) probabilistic choice model that accounts for the effect of the presentation order within a pair.

```
eba.order(M1, M2 = NULL, A = 1:I, s = c(rep(1/J, J), 1),
constrained = TRUE)
## S3 method for class 'eba.order'
summary(object, ...)
```

`M1, M2` |
two square matrices or data frames consisting of absolute choice frequencies in both within-pair orders; row stimuli are chosen over column stimuli. If M2 is empty (default), M1 is assumed to be a 3d array containing both orders |

`A` |
see |

`s` |
the starting vector with default |

`constrained` |
see |

`object` |
an object of class |

`...` |
additional arguments |

The choice models include a single multiplicative order effect,
`order`

, that is constant for all pairs (see Davidson and Beaver,
1977). An order effect < 1 (> 1) indicates a bias in favor of the first
(second) interval. See `eba`

for choice models without order
effect.

Several likelihood ratio tests are performed (see also
`summary.eba`

).

`EBA.order`

tests an order-effect EBA model against a saturated
binomial model; this corresponds to a goodness of fit test of the former
model.

`Order`

tests an EBA model with an order effect constrained to 1
against an unconstrained order-effect EBA model; this corresponds to a test
of the order effect.

`Effect`

tests an order-effect indifference model (where all scale
values are equal, but the order effect is free) against the order-effect EBA
model; this corresponds to testing for a stimulus effect; `order0`

is
the estimate of the former model.

Wickelmaier and Choisel (2006) describe a model that generalizes the Davidson-Beaver model and allows for an order effect in Pretree and EBA models.

`coefficients` |
a vector of parameter estimates, the last component holds the order-effect estimate |

`estimate` |
same as |

`logL.eba` |
the log-likelihood of the fitted model |

`logL.sat` |
the log-likelihood of the saturated (binomial) model |

`goodness.of.fit` |
the goodness of fit statistic including the likelihood ratio fitted vs. saturated model (-2logL), the degrees of freedom, and the p-value of the corresponding chi-square distribution |

`u.scale` |
the unnormalized utility scale of the stimuli; each utility scale value is defined as the sum of aspect values (parameters) that characterize a given stimulus |

`hessian` |
the Hessian matrix of the likelihood function |

`cov.p` |
the covariance matrix of the model parameters |

`chi.alt` |
the Pearson chi-square goodness of fit statistic |

`fitted` |
3d array of the fitted paired-comparison matrices |

`y1` |
the data vector of the upper triangle matrices |

`y0` |
the data vector of the lower triangle matrices |

`n` |
the number of observations per pair ( |

`mu` |
the predicted choice probabilities for the upper triangles |

`M1, M2` |
the data matrices |

Florian Wickelmaier

Davidson, R.R., & Beaver, R.J. (1977).
On extending the Bradley-Terry model to incorporate within-pair order
effects.
*Biometrics*, **33**, 693–702.

Wickelmaier, F., & Choisel, S. (2006).
Modeling within-pair order effects in paired-comparison judgments.
In D.E. Kornbrot, R.M. Msetfi, & A.W. MacRae (eds.),
*Fechner Day 2006. Proceedings of the 22nd Annual Meeting of
the International Society for Psychophysics* (p. 89–94).
St. Albans, UK: The ISP.

`eba`

, `group.test`

, `plot.eba`

,
`residuals.eba`

, `logLik.eba`

.

```
data(heaviness) # weights judging data
ebao1 <- eba.order(heaviness) # Davidson-Beaver model
summary(ebao1) # goodness of fit
plot(ebao1) # residuals versus predicted values
confint(ebao1) # confidence intervals for parameters
```

[Package *eba* version 1.10-0 Index]