drda {drda} | R Documentation |

Use the Newton's with a trust-region method to fit non-linear growth curves to observed data.

```
drda(
formula,
data,
subset,
weights,
na.action,
mean_function = "logistic4",
is_log = TRUE,
lower_bound = NULL,
upper_bound = NULL,
start = NULL,
max_iter = 10000
)
```

`formula` |
an object of class |

`data` |
an optional data frame, list or environment (or object coercible
by |

`subset` |
an optional vector specifying a subset of observations to be used in the fitting process. |

`weights` |
an optional vector of weights to be used in the fitting
process. If provided, weighted least squares is used with weights |

`na.action` |
a function which indicates what should happen when the data
contain |

`mean_function` |
the model to be fitted. See |

`is_log` |
a logical value indicating whether the predictor variable |

`lower_bound` |
numeric vector with the minimum admissible values of the
parameters. Use |

`upper_bound` |
numeric vector with the maximum admissible values of the
parameters. Use |

`start` |
starting values for the parameters. |

`max_iter` |
maximum number of iterations in the optimization algorithm. |

The most general model in this package is the generalized logistic function
selected by setting `mean_function = "logistic6"`

. It is defined in this
package as the 6-parameter function

`alpha + (beta - alpha) / (xi + nu * exp(-eta * (x - phi)))^(1 / nu)`

where `eta != 0`

, `nu > 0`

, and `xi > 0`

. Although `beta`

can be any real
value, we use the convention `beta > alpha`

to avoid identifiability
problems: when `beta < alpha`

it is always possible to adjust the other
parameters to obtain the same exact curve. When `beta > alpha`

and `eta > 0`

the curve is monotonically increasing. If `beta > alpha`

and `eta < 0`

the
curve is monotonically decreasing.

Parameter `alpha`

represents the lower horizontal asymptote of the curve.
Parameter `beta`

is related to the upper horizontal asymptote of the curve.
Parameter `eta`

represents the steepness (growth rate) of the curve.
Parameter `phi`

is related to the value of the function at `x = 0`

.
Parameter `nu`

affects near which asymptote maximum growth occurs.
Parameter `xi`

affects the value of the upper asymptote.

**Note**: the 6-parameter logistic function is non-identifiable from data and
should not be used in real applications. It is available only for theoretical
research convenience.

The 5-parameter logistic function can be selected by choosing
`mean_function = "logistic5"`

. The function is obtained by setting `xi = 1`

in the generalized logistic function, that is

`alpha + (beta - alpha) / (1 + nu * exp(-eta * (x - phi)))^(1 / nu)`

Parameter `alpha`

represents the lower horizontal asymptote of the curve.
Parameter `beta`

represents the upper horizontal asymptote of the curve.
Parameter `eta`

represents the steepness (growth rate) of the curve.
Parameter `phi`

is related to the value of the function at `x = 0`

.
Parameter `nu`

affects near which asymptote maximum growth occurs.

The 4-parameter logistic function is the default model of `drda`

. It can be
explicitly selected by choosing `mean_function = "logistic4"`

. The function
is obtained by setting `xi = 1`

and `nu = 1`

in the generalized logistic
function, that is

`alpha + (beta - alpha) / (1 + exp(-eta * (x - phi)))`

Parameter `alpha`

represents the lower horizontal asymptote of the curve.
Parameter `beta`

represents the upper horizontal asymptote of the curve.
Parameter `eta`

represents the steepness (growth rate) of the curve.
Parameter `phi`

represents the `x`

value at which the curve is equal to its
mid-point, i.e. `f(phi; alpha, beta, eta, phi) = (alpha + beta) / 2`

.

The 2-parameter logistic function can be selected by choosing
`mean_function = "logistic2"`

. The function is obtained by setting `xi = 1`

,
`nu = 1`

, `beta = 1`

, and `alpha = 0`

in the generalized logistic function,
that is

`1 / (1 + exp(-eta * (x - phi)))`

Parameter `eta`

represents the steepness (growth rate) of the curve.
Parameter `phi`

represents the `x`

value at which the curve is equal to its
mid-point, i.e. `f(phi; eta, phi) = 1 / 2`

.

The Gompertz function is the limit for `nu -> 0`

of the 5-parameter logistic
function. It can be selected by choosing `mean_function = "gompertz"`

. The
function is defined in this package as

`alpha + (beta - alpha) * exp(-exp(-eta * (x - phi)))`

where `eta != 0`

.

Parameter `alpha`

represents the lower horizontal asymptote of the curve.
Parameter `beta`

represents the upper horizontal asymptote of the curve.
Parameter `eta`

represents the steepness (growth rate) of the curve.
Parameter `phi`

is related to the value of the function at `x = 0`

.

It is possible to search for the maximum likelihood estimates within
pre-specified interval regions. Since the upper horizontal asymptote `beta`

must be greater than the lower horizontal asymptote `alpha`

, intervals are
adjusted to satisfy this constraint.

*Note*: Hypothesis testing is not available for constrained estimates
because asymptotic approximations might not be valid

An object of class `drda`

and `model_fit`

, where `model`

is the
chosen mean function. It is a list containing the following components:

- converged
boolean value assessing if the optimization algorithm converged or not.

- iterations
total number of iterations performed by the optimization algorithm

- constrained
boolean value set to

`TRUE`

if optimization was constrained.- estimated
boolean vector indicating which parameters were estimated from the data.

- coefficients
maximum likelihood estimates of the model parameters.

- rss
minimum value (found) of the residual sum of squares.

- df.residuals
residual degrees of freedom.

- fitted.values
fitted mean values.

- residuals
residuals, that is response minus fitted values.

- weights
(only for weighted fits) the specified weights.

- mean_function
model that was used for fitting.

- n
effective sample size.

- sigma
corrected maximum likelihood estimate of the standard deviation.

- loglik
maximum value (found) of the log-likelihood function.

- fisher.info
observed Fisher information matrix evaluated at the maximum likelihood estimator.

- vcov
approximate variance-covariance matrix of the model parameters.

- call
the matched call.

- terms
the

`terms`

object used.- model
the model frame used.

- na.action
(where relevant) information returned by

`model.frame`

on the special handling of`NA`

s.- is_log
boolean value. It is

`TRUE`

if the predictor variable was given on the log scale.

[Package *drda* version 1.0.0 Index]