india (version 0.1-2)

logLik.displacement: 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 lm
logLik.displacement(model, pars = "full", ...)
# S3 method for ols
logLik.displacement(model, pars = "full", ...)
# S3 method for nls
logLik.displacement(model, ...)
# S3 method for lad
logLik.displacement(model, method = "quasi", pars = "full", ...)
# S3 method for ridge
logLik.displacement(model, pars = "full", ...)

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

$$LD_i(\bold{\beta}|\sigma^2) = 2\{l(\hat{\bold{\beta}},\hat{\sigma}^2) - \max_{\sigma^2} l(\hat{\bold{\beta}}_{(i)},\hat{\sigma}^2)\}.$$

Arguments

model

an R object, returned by lm, nls, ols, lad or ridge.

pars

should be considered the whole vector of parameters (pars = "full"), or only the vector of coefficients (pars = "coef"). This option is not used for nls objects.

method

only required for 'lad' objects, options available are "quasi" and "BR" and "approx" to obtain the likelihood displacement based on Sun and Wei (2004), Elian et al. (2000) approaches, respectively.

...

further arguments passed to or from other methods.

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. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.1080/03610920008832518")

Ogueda, A., Osorio, F. (2025). Influence diagnostics for ridge regression using the Kullback-Leibler divergence. Statistical Papers 66, 85. tools:::Rd_expr_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. tools:::Rd_expr_doi("10.2307/3315198")

Sun, R.B., Wei, B.C. (2004). On influence assessment for LAD regression. Statistics & Probability Letters 67, 97-110. tools:::Rd_expr_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)