# fitbusscher: Self-starting Nls Busscher's (1990) Model for Soil... In soilphysics: Soil Physical Analysis

## Description

Function to self start the nonlinear Busscher's (1990) model for penetration resistance, i.e., Pr = b0 * (θ ^ {b1}) * (Bd ^ {b2}). It creates initial estimates (by log-linearization) of the parameters b0, b1 and b2 and uses them to provide its least-squares estimates through `nls`.

## Usage

 `1` ``` fitbusscher(Pr, theta, Bd, ...) ```

## Arguments

 `Pr` a numeric vector containing penetration resistance values. `theta` a numeric vector containing soil moisture values at which to evaluate the model. `Bd` a numeric vector containing bulk density values at which to evaluate the model. `...` further arguments to `nls`.

## Value

A `nls` output (see `help(nls)`).

## Author(s)

Anderson Rodrigo da Silva <anderson.agro@hotmail.com>

## References

Busscher, W. J. (1990). Adjustment of flat-tipped penetrometer resistance data to common water content. Transactions of the ASAE, 3:519-524.

`fitlbc`, `nls`, `summary.nls`, `predict.nls`, `Rsq`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```data(compaction) attach(compaction) out <- fitbusscher(Pr = PR, theta = Mois, Bd = BD) summary(out) Rsq(out) # 3D plot X <- seq(min(Mois), max(Mois), len = 30) # theta Y <- seq(min(BD), max(BD), len = 30) # Bd f <- function(x, y) coef(out) * (x^coef(out)) * (y^coef(out)) Z <- outer(X, Y, f) persp(X, Y, Z, xlab = "Soil moisture", ylab = "Soil bulk density", zlab = "Penetration resistance", ticktype = "detailed", phi = 20, theta = 30) # End (not run) ```

### Example output ```Loading required package: rpanel
Package `rpanel', version 1.1-4: type help(rpanel) for summary information
---
soilphysics version 3.1

Warning messages:
1: no DISPLAY variable so Tk is not available

Formula: Pr ~ b0 * (theta^b1) * (Bd^b2)

Parameters:
Estimate Std. Error t value Pr(>|t|)
b0   1.1680     0.2618   4.461 5.07e-05 ***
b1  -0.8770     0.2247  -3.903 0.000302 ***
b2   0.1105     0.5399   0.205 0.838741
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.5579 on 47 degrees of freedom

Number of iterations to convergence: 6
Achieved convergence tolerance: 2.675e-06

\$pseudo.R.squared
 0.8961571