Distance based regression models for proportions {Compositional} R Documentation

## Distance based regression models for proportions

### Description

Distance based regression models for proportions.

### Usage

```ols.prop.reg(y, x, cov = FALSE, tol = 1e-07, maxiters = 100)
helling.prop.reg(y, x, tol = 1e-07, maxiters = 100)
```

### Arguments

 `y` A numerical vector proportions. 0s and 1s are allowed. `x` A matrix or a data frame with the predictor variables. `cov` Should the covariance matrix be returned? TRUE or FALSE. `tol` The tolerance value to terminate the Newton-Raphson algorithm. This is set to 10^{-9} by default. `maxiters` The maximum number of iterations before the Newton-Raphson is terminated automatically.

### Details

We are using the Newton-Raphson, but unlike R's built-in function "glm" we do no checks and no extra calculations, or whatever. Simply the model. The functions accept binary responses as well (0 or 1).

### Value

A list including:

 `sse` The sum of squres of errors for the "ols.prop.reg" function. `be` The estimated regression coefficients. `seb` The standard error of the regression coefficients if "cov" is TRUE. `covb` The covariance matrix of the regression coefficients in "ols.prop.reg" if "cov" is TRUE. `H` The Hellinger distance between the true and the obseervd proportions in "helling.prop.reg". `iters` The number of iterations required by the Newton-Raphson.

### Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

### References

Papke L. E. & Wooldridge J. (1996). Econometric methods for fractional response variables with an application to 401(K) plan participation rates. Journal of Applied Econometrics, 11(6): 619–632.

McCullagh, Peter, and John A. Nelder. Generalized linear models. CRC press, USA, 2nd edition, 1989.

``` propreg, beta.reg ```
```y <- rbeta(100, 1, 4)