# cdf.lmscreg: Cumulative Distribution Function for LMS Quantile Regression In VGAM: Vector Generalized Linear and Additive Models

## Description

Computes the cumulative distribution function (CDF) for observations, based on a LMS quantile regression.

## Usage

 `1` ```cdf.lmscreg(object, newdata = NULL, ...) ```

## Arguments

 `object` A VGAM quantile regression model, i.e., an object produced by modelling functions such as `vglm` and `vgam` with a family function beginning with `"lms."`. `newdata` Data frame where the predictions are to be made. If missing, the original data is used. `...` Parameters which are passed into functions such as `cdf.lms.yjn`.

## Details

The CDFs returned here are values lying in [0,1] giving the relative probabilities associated with the quantiles `newdata`. For example, a value near 0.75 means it is close to the upper quartile of the distribution.

## Value

A vector of CDF values lying in [0,1].

## Note

The data are treated like quantiles, and the percentiles are returned. The opposite is performed by `qtplot.lmscreg`.

The CDF values of the model have been placed in `@post\$cdf` when the model was fitted.

Thomas W. Yee

## References

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

`deplot.lmscreg`, `qtplot.lmscreg`, `lms.bcn`, `lms.bcg`, `lms.yjn`.

## Examples

 ```1 2 3 4 5 6 7``` ```fit <- vgam(BMI ~ s(age, df=c(4, 2)), lms.bcn(zero = 1), data = bmi.nz) head(fit@post\$cdf) head(cdf(fit)) # Same head(depvar(fit)) head(fitted(fit)) cdf(fit, data.frame(age = c(31.5, 39), BMI = c(28.4, 24))) ```

### Example output

```Loading required package: stats4
VGAM  s.vam  loop  1 :  loglikelihood = -6429.7568
VGAM  s.vam  loop  2 :  loglikelihood = -6327.3502
VGAM  s.vam  loop  3 :  loglikelihood = -6313.2224
VGAM  s.vam  loop  4 :  loglikelihood = -6312.8069
VGAM  s.vam  loop  5 :  loglikelihood = -6312.8166
VGAM  s.vam  loop  6 :  loglikelihood = -6312.8032
VGAM  s.vam  loop  7 :  loglikelihood = -6312.8088
VGAM  s.vam  loop  8 :  loglikelihood = -6312.8062
VGAM  s.vam  loop  9 :  loglikelihood = -6312.8074
VGAM  s.vam  loop  10 :  loglikelihood = -6312.8068
VGAM  s.vam  loop  11 :  loglikelihood = -6312.8071
VGAM  s.vam  loop  12 :  loglikelihood = -6312.807
1         2         3         4         5         6
0.2280309 0.6365499 0.6356761 0.4321450 0.4321311 0.9686738
1         2         3         4         5         6
0.2280309 0.6365499 0.6356761 0.4321450 0.4321311 0.9686738
[,1]
1 22.77107
2 27.70033
3 28.18127
4 25.08380
5 26.46388
6 36.19648
25%      50%      75%
1 23.00836 25.48922 28.44767
2 23.65211 26.19783 29.23269
3 24.07328 26.66334 29.75085
4 23.25503 25.75937 28.74518
5 24.53531 27.17650 30.32525
6 23.63164 26.17517 29.20742
1         2
0.7469759 0.2861046
```

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.