deltaLN {fishMod}

Fitting models based on the Delta Log-Normal distribution.

Description

Fits a compound model that assumes a Delta Log-Normal distribution. The mean of the log-normal process and the mean of the binary process are allowed to change with covariates.

Usage

deltaLN( ln.form, binary.form, data, residuals=TRUE)

Arguments

ln.form

an object of class "formula" (or one that can be coerced to that class). This is a symbolic representation of the model for the log-normal variable. Note that offset terms (if any) should be included in this part of the model.

binary.form

an object of class "formula" (or one that can be coerced to that class). This is a symbolic representation of the model for the binary variable and should not contain an outcome (e.g. ~1+var1+var2).

data

a data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model.

residuals

boolean indicating if the quantile residuals should be calculated. Default is TRUE indicating residuals are to be calculated.

Details

The observed random variables y_i are assumed to arise from a process that has a non-zero probability that y_i is greater than zero; further, the distribution of y_i conditional on y_i>0 follows a log-normal distribution. This modelling framework models the mean of the conditional distribution and the probability of obtaining a non-zero.

The means of each component of the model are specified in ln.form and binary.form for the log-normal and the zero/non-zero model components respectively. The binary.form formula should not contain an outcome. The binary part of the model is done using a logistic link funciton.

If residuals are requested then two types are returned: Pearson residuals and randomised quantile residuals, described in general by Dunn and Smyth (1996).

Value

pgm returns an object of class "DeltaLNmod", a list with the following elements

coef

the estiamted coefficients from the fitting process. A list with an element for the binary and log-normal parts of the model as well as an element for the standard deviation of the log-normal.

logl

the maximum log likelihood (found at the estimates).

AIC

an Information Criteria.

BIC

Bayesian Information Criteria.

fitted

fitted values of the delta log-normal variable.

fitted.var

variance of the fitted delta log-normal variable.

residuals

a 2-column matrix whose first column contains the randomised quantile residuals and whose second column contains the Pearson residuals.

n

the number of observations used to fit the model.

ncovars

the number of parameters in the combined model.

nzero

the number of non-zero elements.

lnMod

the lm object obtained from fitting the log-normal (non-zero) part of the model.

binMod

the glm object obtained from fitting the zero / non-zero part of the model.

Author(s)

Scott D. Foster

References

Aitchison J. (1955) On the Distribution of a Positive Random Variable Having a Discrete Probability Mass at the Origin. Journal of the American Statistical Association 50 901-908.

Dunn P. K and Smyth G. K (1996) Randomized Quantile Residuals. Journal of Computational and Graphical Statistics 5: 236-244.

Foster, S.D. and Bravington, M.V. (2013) A Poisson-Gamma Model for Analysis of Ecological Non-Negative Continuous Data. Journal of Environmental and Ecological Statistics 20: 533-552