eba.order {eba} | R Documentation |
Elimination-by-Aspects (EBA) Models with Order-Effect
Description
Fits a (multi-attribute) probabilistic choice model that accounts for the effect of the presentation order within a pair.
Usage
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, ...)
Arguments
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 |
Details
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.
Value
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 |
Author(s)
Florian Wickelmaier
References
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.
See Also
eba
, group.test
, plot.eba
,
residuals.eba
, logLik.eba
.
Examples
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