Likedist {influence.SEM} | R Documentation |
Likelihood Distance.
Description
A general model-based measure of case influence on model fit is likelihood distance (Cook, 1977, 1986; Cook & Weisberg, 1982) defined as
LD_i=2[L(\hat{\mathbf{\theta}})-L(\hat{\mathbf{\theta}}_{(i)})]
where \hat{\mathbf{\theta}}
and \hat{\mathbf{\theta}}_{(i)}
are the k \times 1
vectors of estimated model parameters on the original and deleted i
samples, respectively, where i = 1, \ldots, N
. The subscript (i
) indicates that the estimate was computed on the sample excluding case i
. L(\hat{\mathbf{\theta}})
and L(\hat{\mathbf{\theta}}_{(i)})
are the log-likelihoods based on the original and the deleted i
samples, respectively.
Usage
Likedist(model, data, ...)
Arguments
model |
A description of the user-specified model using the lavaan model syntax. See |
data |
A data frame containing the observed variables used in the model. If any variables are declared as ordered factors, this function will treat them as ordinal variables. |
... |
Additional parameters for |
Details
The log-likelihoods L(\hat{\mathbf{\theta}})
and L(\hat{\mathbf{\theta}}_{(i)})
are computed by the function bollen.loglik
using the formula 4B2 described by Bollen (1989, pag. 135).
The likelihood distance gives the amount by which the log-likelihood of the full data changes if one were to evaluate it at the reduced-data estimates. The important point is that L(\hat{\mathbf{\theta}}_{(i)})
is not the log-likelihood obtained by fitting the model to the reduced data set. It is obtained by evaluating the likelihood function based on the full data set (containing all n
observations) at the reduced-data estimates (Schabenberger, 2005).
Value
Returns a vector of LD_i
.
Note
If for observation i
model does not converge or yelds a solution with negative estimated variances, the associated value of LD_i
is set to NA
.
Author(s)
Massimiliano Pastore, Gianmarco Altoe'
References
Bollen, K.A. (1989). Structural Equations with latent Variables. New York, NY: Wiley.
Cook, R.D. (1977). Detection of influential observations in linear regression. Technometrics, 19, 15-18.
Cook, R.D. (1986). Assessment of local influence. Journal of the Royal Statistical Society B, 48, 133-169.
Cook, R.D., Weisberg, S. (1986). Residuals and influence in regressions. New York, NY: Chapman & Hall.
Pek, J., MacCallum, R.C. (2011). Sensitivity Analysis in Structural Equation Models: Cases and Their Influence. Multivariate Behavioral Research, 46, 202-228.
Schabenberger, O. (2005). Mixed model influence diagnostics. In SUGI, 29, 189-29. SAS institute Inc, Cary, NC.
See Also
Examples
## not run: this example take several minutes
data("PDII")
model <- "
F1 =~ y1+y2+y3+y4
"
# fit0 <- sem(model, data=PDII)
# LD <-Likedist(model,data=PDII)
# plot(LD,pch=19,xlab="observations",ylab="Likelihood distances")
## not run: this example take several minutes
## an example in which the deletion of a case yelds a solution
## with negative estimated variances
model <- "
F1 =~ x1+x2+x3
F2 =~ y1+y2+y3+y4
F3 =~ y5+y6+y7+y8
"
# fit0 <- sem(model, data=PDII)
# LD <-Likedist(model,data=PDII)
# plot(LD,pch=19,xlab="observations",ylab="Likelihood distances")