logLik.displacement {india} | R Documentation |
Likelihood Displacement
Description
Compute the likelihood displacement influence measure based on leave-one-out cases deletion for linear models, lad and ridge regression.
Usage
logLik.displacement(model, ...)
## S3 method for class 'lm'
logLik.displacement(model, pars = "full", ...)
## S3 method for class 'nls'
logLik.displacement(model, ...)
## S3 method for class 'ols'
logLik.displacement(model, pars = "full", ...)
## S3 method for class 'lad'
logLik.displacement(model, method = "quasi", pars = "full", ...)
## S3 method for class 'ridge'
logLik.displacement(model, pars = "full", ...)
Arguments
model |
|
pars |
should be considered the whole vector of parameters ( |
method |
only required for |
... |
further arguments passed to or from other methods. |
Value
A vector whose ith element contains the distance between the likelihood functions,
LD_i(\bold{\beta},\sigma^2) = 2\{l(\hat{\bold{\beta}},\hat{\sigma}^2) -
l(\hat{\bold{\beta}}_{(i)},\hat{\sigma}^2_{(i)})\},
for pars = "full"
, where \hat{\bold{\beta}}_{(i)}
and \hat{\sigma}^2_{(i)}
denote the estimates of \bold{\beta}
and \sigma^2
when the ith observation is
removed from the dataset. If we are interested only in \bold{\beta}
(i.e. pars = "coef"
)
the likelihood displacement becomes
LD_i(\bold{\beta}|\sigma^2) = 2\{l(\hat{\bold{\beta}},\hat{\sigma}^2) -
\max_{\sigma^2} l(\hat{\bold{\beta}}_{(i)},\hat{\sigma}^2)\}.
References
Cook, R.D., Weisberg, S. (1982). Residuals and Influence in Regression. Chapman and Hall, London.
Cook, R.D., Pena, D., Weisberg, S. (1988). The likelihood displacement: A unifying principle for influence measures. Communications in Statistics - Theory and Methods 17, 623-640. doi:10.1080/03610928808829645
Elian, S.N., Andre, C.D.S., Narula, S.C. (2000). Influence measure for the L1 regression. Communications in Statistics - Theory and Methods 29, 837-849. doi:10.1080/03610920008832518
Ogueda, A., Osorio, F. (2025). Influence diagnostics for ridge regression using the Kullback-Leibler divergence. Statistical Papers 66, 85. doi:10.1007/s00362-025-01701-1
Ross, W.H. (1987). The geometry of case deletion and the assessment of influence in nonlinear regression. The Canadian Journal of Statistics 15, 91-103. doi:10.2307/3315198
Sun, R.B., Wei, B.C. (2004). On influence assessment for LAD regression. Statistics & Probability Letters 67, 97-110. doi:10.1016/j.spl.2003.08.018
Examples
# Likelihood displacement for linear regression
fm <- ols(stack.loss ~ ., data = stackloss)
LD <- logLik.displacement(fm)
plot(LD, ylab = "Likelihood displacement", ylim = c(0,9))
text(21, LD[21], label = as.character(21), pos = 3)
# Likelihood displacement for LAD regression
fm <- lad(stack.loss ~ ., data = stackloss)
LD <- logLik.displacement(fm)
plot(LD, ylab = "Likelihood displacement", ylim = c(0,1.5))
text(17, LD[17], label = as.character(17), pos = 3)
# Likelihood displacement for ridge regression
data(portland)
fm <- ridge(y ~ ., data = portland)
LD <- logLik.displacement(fm)
plot(LD, ylab = "Likelihood displacement", ylim = c(0,4))
text(8, LD[8], label = as.character(8), pos = 3)
# Likelihood displacement for nonlinear regression
data(skeena)
model <- recruits ~ b1 * spawners * exp(-b2 * spawners)
fm <- nls(model, data = skeena, start = list(b1 = 3, b2 = 0))
LD <- logLik.displacement(fm)
plot(LD, ylab = "Likelihood displacement", ylim = c(0,0.7))
obs <- c(5, 6, 9, 19, 25)
text(obs, LD[obs], label = as.character(obs), pos = 3)