lms.bcg {VGAM} | R Documentation

## LMS Quantile Regression with a Box-Cox transformation to a Gamma Distribution

### Description

LMS quantile regression with the Box-Cox transformation to the gamma distribution.

### Usage

    lms.bcg(percentiles = c(25, 50, 75), zero = c("lambda", "sigma"),
            llambda = "identitylink", lmu = "identitylink", lsigma = "loge",
            idf.mu = 4, idf.sigma = 2, ilambda = 1, isigma = NULL)

### Arguments

`percentiles` | A numerical vector containing values between 0 and 100, which are the quantiles. They will be returned as ‘fitted values’.
`zero` | See `lms.bcn`.
`llambda, lmu, lsigma` | See `lms.bcn`.
`idf.mu, idf.sigma` | See `lms.bcn`.
`ilambda, isigma` | See `lms.bcn`.

### Details

Given a value of the covariate, this function applies a Box-Cox transformation to the response to best obtain a gamma distribution. The parameters chosen to do this are estimated by maximum likelihood or penalized maximum likelihood. Similar details can be found at `lms.bcn`.

### Value

An object of class `"vglmff"` (see `vglmff-class`). The object is used by modelling functions such as `vglm`, `rrvglm` and `vgam`.

### Warning

This VGAM family function comes with the same warnings as `lms.bcn`. Also, the expected value of the second derivative with respect to lambda may be incorrect (my calculations do not agree with the Lopatatzidis and Green manuscript.)

### Note

Similar notes can be found at `lms.bcn`.

### Author(s)

Thomas W. Yee

### References

Lopatatzidis A. and Green, P. J. (unpublished manuscript) Semiparametric quantile regression using the gamma distribution.

Yee, T. W. (2004) Quantile regression via vector generalized additive models. Statistics in Medicine, 23, 2295–2315.

### See Also

`lms.bcn`, `lms.yjn`, `qtplot.lmscreg`, `deplot.lmscreg`, `cdf.lmscreg`, `bmi.nz`, `amlexponential`.

### Examples

    # This converges, but deplot(fit) and qtplot(fit) do not work
    fit0 <- vglm(BMI ~ sm.bs(age, df = 4), lms.bcg, data = bmi.nz, trace = TRUE)
    coef(fit0, matrix = TRUE)
    ## Not run:
    par(mfrow = c(1, 1))
    plotvgam(fit0, se = TRUE)  # Plot mu function (only)

    ## End(Not run)

    # Use a trick: fit0 is used for initial values for fit1.
    fit1 <- vgam(BMI ~ s(age, df = c(4, 2)), etastart = predict(fit0),
                 lms.bcg(zero = 1), bmi.nz, trace = TRUE)

    # Difficult to get a model that converges.
    # Here, we prematurely stop iterations because it fails near the solution.
    fit2 <- vgam(BMI ~ s(age, df = c(4, 2)), maxit = 4,
                 lms.bcg(zero = 1, ilam = 3), bmi.nz, trace = TRUE)
    summary(fit1)
    head(predict(fit1))
    head(fitted(fit1))
    head(bmi.nz)
    # Person 1 is near the lower quartile of BMI amongst people his age
    head(cdf(fit1))

    ## Not run:
    # Quantile plot
    par(bty = "l", mar=c(5, 4, 4, 3) + 0.1, xpd = TRUE)
    qtplot(fit1, percentiles=c(5, 50, 90, 99), main = "Quantiles",
           xlim = c(15, 90), las = 1, ylab = "BMI", lwd = 2, lcol = 4)

    # Density plot
    ygrid <- seq(15, 43, len = 100)  # BMI ranges
    par(mfrow = c(1, 1), lwd = 2)
    (aa <- deplot(fit1, x0 = 20, y = ygrid, xlab = "BMI", col = "black",
      main = "Density functions at Age = 20 (black), 42 (red) and 55 (blue)"))
    aa <- deplot(fit1, x0=42, y=ygrid, add=TRUE, llty=2, col="red")
    aa <- deplot(fit1, x0=55, y=ygrid, add=TRUE, llty=4, col="blue", Attach=TRUE)
    aa@post$deplot  # Contains density function values

    ## End(Not run)

[Package VGAM version 1.0-4 Index]