Maximum likelihood estimation of the 1-parameter extended log-F distribution.
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Numeric, the desired quantiles. A strictly increasing sequence,
each value must be in (0, 1).
The default values are the three quartiles, matching
Numeric, both of unit length and nonnegative,
the separation and shift parameters.
If avoiding the quantile crossing problem is of concern to you,
Positive tuning parameter which controls the sharpness of the cusp.
The limit as it approaches 0 is probably very similar to
Positive scale parameter and sometimes called
Either the value 1, 2, or ....
This is an experimental family function for quantile regression.
Fasiolo et al. (2020) propose an extended log-F distribution
however this family function only estimates the location parameter.
The distribution has a scale parameter which can be inputted
(default value is unity).
One location parameter is estimated for each
and these are the estimated quantiles.
For quantile regression it is not necessary to estimate
the scale parameter since the log-likelihood function is
The ELF is used as an approximation of the asymmetric Laplace
The latter cannot be estimated properly using Fisher scoring/IRLS
but the ELF holds promise because it has continuous derivatives
and therefore fewer problems with the regularity conditions.
Because the ELF is fitted to data to obtain an
empirical result the convergence behaviour may not be gentle
Hence there is a function-specific control function called
extlogF1.control which has something like
stepsize = 0.5 and
maxits = 100.
It has been found that
slowing down the rate of convergence produces greater
stability during the estimation process.
Regardless, convergence should be monitored carefully always.
This function accepts a vector response but not a matrix response.
An object of class
The object is used by modelling functions such as
Changes will occur in the future to fine-tune things.
trace = TRUE is strongly encouraged because it is
needful to check that convergence occurs properly.
seppar > 0 then
logLik(fit) will return the
Thomas W. Yee
Fasiolo, M., Wood, S. N., Zaffran, M., Nedellec, R. and Goude, Y. (2020). Fast calibrated additive quantile regression. J. Amer. Statist. Assoc., in press.
Yee, T. W. (2020). On quantile regression based on the 1-parameter extended log-F distribution. In preparation.
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nn <- 1000; mytau <- c(0.25, 0.75) edata <- data.frame(x2 = sort(rnorm(nn))) edata <- transform(edata, y1 = 1 + x2 + rnorm(nn, sd = exp(-1)), y2 = cos(x2) / (1 + abs(x2)) + rnorm(nn, sd = exp(-1))) fit1 <- vglm(y1 ~ x2, extlogF1(tau = mytau), data = edata) # trace = TRUE fit2 <- vglm(y2 ~ bs(x2, 6), extlogF1(tau = mytau), data = edata) coef(fit1, matrix = TRUE) fit2@extra$percentile # Empirical percentiles here summary(fit2) c(is.crossing(fit1), is.crossing(fit2)) head(fitted(fit1)) ## Not run: plot(y2 ~ x2, edata, col = "blue") matlines(with(edata, x2), fitted(fit2), col="orange", lty = 1, lwd = 2) ## End(Not run)
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