Package 'oneinfl' reference manual

Title:	Estimates OIPP and OIZTNB Regression Models
Description:	Estimates one-inflated positive Poisson (OIPP) and one-inflated zero-truncated negative binomial (OIZTNB) regression models. A suite of ancillary statistical tools are also provided, including: estimation of positive Poisson (PP) and zero-truncated negative binomial (ZTNB) models; marginal effects and their standard errors; diagnostic likelihood ratio and Wald tests; plotting; predicted counts and expected responses; and random variate generation. The models and tools, as well as four applications, are shown in Godwin, R. T. (2024). "One-inflated zero-truncated count regression models" arXiv preprint <arXiv:2402.02272>.
Authors:	Ryan T. Godwin [aut, cre]
Maintainer:	Ryan T. Godwin <[email protected]>
License:	GPL (>= 3)
Version:	1.0.0
Built:	2025-03-09 05:41:07 UTC
Source:	https://github.com/rtgodwin/oneinfl

Compute Marginal Effects for One-inflated models

Description

This wrapper function calls a different function to calculate marginal effects depending on the model type. The marginal effects of the variables are evaluated at specified points, such as the sample means or averages, or at custom-defined cases.

Usage

margins(model, df, at = "AE")
margins(model, df, at = "AE")

Arguments

model

An object representing a fitted model. Must be of class oneinflmodel or truncmodel.

df

A data.frame containing the dataset used to fit the model. The variables in the data must match those used in the model.

at

A character string or list specifying where to evaluate the marginal effects:

"AE": Average Effect (marginal effect averaged over all data points; default).
"EM": Effect at Means (marginal effect evaluated at the sample means of the data).
A named list: A custom case specifying representative values for variables.

Details

The function computes marginal effects for zero-truncated Poisson or negative binomial regression models. It handles different model types; oneinflmodel for one-inflated models, and truncmodel for standard count models. The marginal effects are evaluated at either all data points and averaged (AE, the default), at the sample means of the variables (EM), or at a custom case. The marginal effects for dummy variables are actually the differences in expected outcomes for values of the dummy of 1 and 0. The marginal effects are displayed along with their statistical significance, evaluated based on the chosen at parameter.

Value

Prints the marginal effects, their standard errors, z-values, p-values, and significance levels.

Examples

df <- data.frame(x = rnorm(100), z = rnorm(100), y = rpois(100, lambda = 5))
model <- oneinfl(y ~ x | z, df = df, dist = "Poisson")
margins(model, df, at = "AE") # Average Effect
margins(model, df, at = "EM") # Effect at Means
margins(model, df, at = list(x = 1, z = 0)) # Custom case

df <- data.frame(x = rnorm(100), z = rnorm(100), y = rpois(100, lambda = 5))
model <- oneinfl(y ~ x | z, df = df, dist = "Poisson")
margins(model, df, at = "AE") # Average Effect
margins(model, df, at = "EM") # Effect at Means
margins(model, df, at = list(x = 1, z = 0)) # Custom case

One-Inflated Regression Model

Description

Fits a one-inflated positive Poisson (OIPP) or one-inflated zero-truncated negative binomial (OIZTNB) regression model.

Usage

oneinfl(formula, df, dist = "negbin", start = NULL, method = "BFGS")
oneinfl(formula, df, dist = "negbin", start = NULL, method = "BFGS")

Arguments

`formula`	A symbolic description of the model to be fitted. Variables before the pipe `\|` link to the usual Poisson rate parameter, after the pipe link to the one-inflation parameter.
`df`	A data frame containing the variables in the model.
`dist`	A character string specifying the distribution to use. Options are `"Poisson"` or `"negbin"`.
`start`	Optional. A numeric vector of starting values for the optimization process. Defaults to `NULL`, in which case starting values are attempted to be chosen automatically.
`method`	A character string specifying the optimization method to be passed to `optim`. Defaults to `"BFGS"`.

Details

This function fits a regression model for one-inflated counts. One-inflated models are used when there are an excess number of ones, relative to a Poisson or negative binomial process.

The function supports two distributions:

"Poisson": One-inflated Poisson regression.
"negbin": One-inflated negative binomial regression.

The function uses numerical optimization via optim to estimate the parameters.

Value

An object of class "oneinflmodel" containing the following components:

beta: Estimated coefficients for the rate component of the model.
gamma: Estimated coefficients for the one-inflation component of the model.
alpha: Dispersion parameter (only for negative binomial distribution).
vc: Variance-covariance matrix of the estimated parameters.
logl: Log-likelihood of the fitted model.
avgw: Average one-inflation probability.
absw: Mean absolute one-inflation probability.
dist: The distribution used for the model ("Poisson" or "negbin").
formula: The formula used for the model.

Examples

# Example usage
df <- data.frame(x = rnorm(100), z = rnorm(100), y = rpois(100, lambda = 1) + 1)
model <- oneinfl(y ~ x | z, df = df, dist = "Poisson")
summary(model)
margins(model, df)
oneWald(model)
predict(model, df)

# Example usage
df <- data.frame(x = rnorm(100), z = rnorm(100), y = rpois(100, lambda = 1) + 1)
model <- oneinfl(y ~ x | z, df = df, dist = "Poisson")
summary(model)
margins(model, df)
oneWald(model)
predict(model, df)

Likelihood Ratio Test for Nested Models

Description

Performs a likelihood ratio test (LRT) to compare two nested models estimated by oneinfl or truncreg. It calculates the LRT statistic and its associated p-value, testing whether the more complex model provides a significantly better fit to the data than the simpler model.

Usage

oneLRT(mod0, mod1)
oneLRT(mod0, mod1)

Arguments

`mod0`	A model object (typically the simpler model) estimated using `oneinfl` or `truncreg`.
`mod1`	A model object (typically the more complex model) estimated using `oneinfl` or `truncreg`.

Details

The function extracts the log-likelihoods and number of parameters from the two models. It then calculates the LRT statistic:

$-2 \cdot (\ell_0 - \ell_1)$

where $\ell_0$ and $\ell_1$ are the log-likelihoods of the simpler and more complex models, respectively. The degrees of freedom for the test are equal to the difference in the number of parameters between the models.

The likelihood ratio test is commonly used to test for:

Overdispersion: Comparing a Poisson model to a negative binomial model.
One-inflation: Comparing a one-inflated model to a non-one-inflated model.

Value

A list with the following components:

LRTstat: The likelihood ratio test statistic.
pval: The p-value associated with the test statistic, based on a chi-squared distribution.

Examples


# Example: One-inflation test
df <- data.frame(y = rpois(100, lambda = 5), x = rnorm(100), z = rnorm(100))
OIZTNB <- oneinfl(y ~ x | z, df = df, dist = "negbin")
ZTNB <- truncreg(y ~ x, df = df, dist = "negbin")
oneLRT(OIZTNB, ZTNB)

# Example: Overdispersion test
OIPP <- oneinfl(y ~ x | z, df = df, dist = "Poisson")
oneLRT(OIZTNB, OIPP)

# Example: One-inflation test
df <- data.frame(y = rpois(100, lambda = 5), x = rnorm(100), z = rnorm(100))
OIZTNB <- oneinfl(y ~ x | z, df = df, dist = "negbin")
ZTNB <- truncreg(y ~ x, df = df, dist = "negbin")
oneLRT(OIZTNB, ZTNB)

# Example: Overdispersion test
OIPP <- oneinfl(y ~ x | z, df = df, dist = "Poisson")
oneLRT(OIZTNB, OIPP)

Plot Observed Data and Model Predictions

Description

Generates a bar plot of observed count data and overlays predicted values from one or more models fitted using oneinfl or truncreg.

Usage

oneplot(model1, model2, model3, model4, df, maxpred, ylimit, ccex)
oneplot(model1, model2, model3, model4, df, maxpred, ylimit, ccex)

Arguments

`model1`	The first fitted model object, either a one-inflated model (class `"oneinflmodel"`) or a truncated model (class `"truncmodel"`).
`model2`	Optional. A second fitted model object, structured similarly to `model1`.
`model3`	Optional. A third fitted model object, structured similarly to `model1`.
`model4`	Optional. A fourth fitted model object, structured similarly to `model1`.
`df`	A data frame containing the variables used in the models.
`maxpred`	Optional. The maximum count value to include in the plot. Defaults to the maximum observed count.
`ylimit`	Optional. The upper limit for the y-axis. Defaults to 1.1 times the highest observed frequency.
`ccex`	Optional. A numeric value controlling the size of plot points and lines. Defaults to `1.5`.

Details

This function visualizes observed count data as a bar plot and overlays predicted values from up to four models. The function automatically detects the type of model (Poisson or negative binomial; one-inflated or truncated) and adjusts the plot accordingly. Predictions are generated using the pred function.

Model types are distinguished by different point and line styles:

Poisson (PP): Dark magenta, triangle-down
Zero-truncated negative binomial (ZTNB): Red, diamond
One-inflated Poisson (OIPP): Green, triangle-up
One-inflated zero-truncated negative binomial (OIZTNB): Blue, circle

The legend in the top-right corner of the plot indicates the models displayed.

Value

A plot is generated but no values are returned.

Examples

# Example usage
df <- data.frame(x = rnorm(100), z = rnorm(100), y = rpois(100, lambda = 5) + 1)
model1 <- oneinfl(y ~ x | z, df = df, dist = "Poisson")
model2 <- truncreg(y ~ x, df = df, dist = "negbin")
oneplot(model1, model2, df = df, maxpred = 10)

# Example usage
df <- data.frame(x = rnorm(100), z = rnorm(100), y = rpois(100, lambda = 5) + 1)
model1 <- oneinfl(y ~ x | z, df = df, dist = "Poisson")
model2 <- truncreg(y ~ x, df = df, dist = "negbin")
oneplot(model1, model2, df = df, maxpred = 10)

Wald Test for One-Inflation

Description

Performs a Wald test to evaluate the significance of the one-inflation parameters in a model estimated using oneinfl.

Usage

oneWald(model)
oneWald(model)

Arguments

model

A model object of class "oneinflmodel" estimated using oneinfl. The model must include one-inflation parameters (gamma) and a variance-covariance matrix (vc).

Details

The Wald test evaluates the null hypothesis that all one-inflation parameters (gamma) are equal to zero, indicating no one-inflation. The test statistic is calculated as:

$W = \gamma^\top V^{-1} \gamma$

where $\gamma$ is the vector of one-inflation parameters and $V$ is their variance-covariance matrix. The p-value is computed using a chi-squared distribution with degrees of freedom equal to the length of $\gamma$ .

This test is commonly used to determine whether a one-inflated model provides a significantly better fit than a non-one-inflated counterpart.

Value

A list with the following components:

W: The Wald test statistic.
pval: The p-value associated with the test statistic, based on a chi-squared distribution.

Examples

# Example usage
df <- data.frame(y = rpois(100, lambda = 5), x = rnorm(100), z = rnorm(100))
OIZTNB <- oneinfl(y ~ x | z, df = df, dist = "negbin")
oneWald(OIZTNB)

# Example usage
df <- data.frame(y = rpois(100, lambda = 5), x = rnorm(100), z = rnorm(100))
OIZTNB <- oneinfl(y ~ x | z, df = df, dist = "negbin")
oneWald(OIZTNB)

Predicted Expected Response for One-Inflated or Truncated Models

Description

Calculates the predicted expected response for a model fitted using oneinfl or truncreg.

Usage

## S3 method for class 'oneinflmodel'
predict(model, df, type = "response")
## S3 method for class 'oneinflmodel'
predict(model, df, type = "response")

Arguments

`model`	A fitted model object of class `"oneinflmodel"` or `"truncmodel"`.
`df`	A data frame containing the predictor variables used in the model.
`type`	A character string specifying the type of prediction. Currently, only `"response"` is supported, which calculates the expected value of the response variable.

Details

This function computes the expected response based on the fitted model. The computation differs depending on the distribution. For Poisson (OIPP), predicted values are computed using E_pois. For Negative Binomial (OIZTNB), predicted values are computed using E_negbin.

Value

A numeric vector of predicted expected responses for the observations in df.

Examples

# Example usage
df <- data.frame(x = rnorm(100), z = rnorm(100), y = rpois(100, lambda = 5))
model <- oneinfl(y ~ x | z, df = df, dist = "Poisson")
predict(model, df = df, type = "response")

# Example usage
df <- data.frame(x = rnorm(100), z = rnorm(100), y = rpois(100, lambda = 5))
model <- oneinfl(y ~ x | z, df = df, dist = "Poisson")
predict(model, df = df, type = "response")

Predicted Expected Response for One-Inflated or Truncated Models

Description

Calculates the predicted expected response for a model fitted using oneinfl or truncreg.

Usage

## S3 method for class 'truncmodel'
predict(model, df, type = "response")
## S3 method for class 'truncmodel'
predict(model, df, type = "response")

Arguments

`model`	A fitted model object of class `"oneinflmodel"` or `"truncmodel"`.
`df`	A data frame containing the predictor variables used in the model.
`type`	A character string specifying the type of prediction. Currently, only `"response"` is supported, which calculates the expected value of the response variable.

Details

This function computes the expected response based on the fitted model. The computation differs depending on the distribution. For Poisson (PP), predicted values are computed using E_pois_noinfl. For Negative Binomial (ZTNB), predicted values are computed using E_negbin_noinfl.

Value

A numeric vector of predicted expected responses for the observations in df.

Examples

# Example usage
df <- data.frame(x = rnorm(100), y = rpois(100, lambda = 5))
model <- truncreg(y ~ x, df = df, dist = "Poisson")
predict(model, df = df, type = "response")

# Example usage
df <- data.frame(x = rnorm(100), y = rpois(100, lambda = 5))
model <- truncreg(y ~ x, df = df, dist = "Poisson")
predict(model, df = df, type = "response")

Generate Random Counts from a One-Inflated Poisson Process

Description

Simulates count data from a one-inflated Poisson process using specified parameters for the rate and one-inflation components.

Usage

roipp(b, g, X, Z)
roipp(b, g, X, Z)

Arguments

`b`	A numeric vector of coefficients for the rate component.
`g`	A numeric vector of coefficients for the one-inflation component.
`X`	A matrix or data frame of predictor variables for the rate component.
`Z`	A matrix or data frame of predictor variables for the one-inflation component.

Details

This function generates count data from a one-inflated Poisson process. The process combines:

A Poisson distribution for counts greater than one.
A one-inflation component that adjusts the probability of observing a count of one.

The algorithm:

Calculates the rate parameter ( $\lambda$ ) as $\exp(X \cdot b)$ .
Computes the one-inflation probabilities ( $\omega$ ) based on $Z \cdot g$ .
Simulates counts for each observation:
- Draws a random number to determine whether the count is one.
- Iteratively calculates probabilities for higher counts until the random number is matched.

This function is useful for generating synthetic data for testing or simulation studies involving one-inflated Poisson models.

Value

A numeric vector of simulated count data.

Examples

# Example usage
set.seed(123)
X <- matrix(rnorm(100), ncol = 2)
Z <- matrix(rnorm(100), ncol = 2)
b <- c(0.5, -0.2)
g <- c(1.0, 0.3)
simulated_data <- roipp(b, g, X, Z)
print(simulated_data)

# Example usage
set.seed(123)
X <- matrix(rnorm(100), ncol = 2)
Z <- matrix(rnorm(100), ncol = 2)
b <- c(0.5, -0.2)
g <- c(1.0, 0.3)
simulated_data <- roipp(b, g, X, Z)
print(simulated_data)

Generate Random Counts from a One-Inflated Zero-Truncated Negative Binomial Process

Description

Simulates count data from a one-inflated, zero-truncated negative binomial (OIZTNB) process using specified parameters for the rate, one-inflation, and dispersion components.

Usage

roiztnb(b, g, alpha, X, Z)
roiztnb(b, g, alpha, X, Z)

Arguments

`b`	A numeric vector of coefficients for the rate component.
`g`	A numeric vector of coefficients for the one-inflation component.
`alpha`	A numeric value representing the dispersion parameter for the negative binomial distribution.
`X`	A matrix or data frame of predictor variables for the rate component.
`Z`	A matrix or data frame of predictor variables for the one-inflation component.

Details

This function generates count data from a one-inflated, zero-truncated negative binomial process. The process combines:

A negative binomial distribution for counts greater than one.
A one-inflation component that adjusts the probability of observing a count of one.

The algorithm:

Calculates the rate parameter ( $\lambda$ ) as $\exp(X \cdot b)$ .
Computes the one-inflation probabilities ( $\omega$ ) based on $Z \cdot g$ .
Computes the negative binomial dispersion parameter ( $\theta = \lambda / \alpha$ ).
Simulates counts for each observation:
- Draws a random number to determine whether the count is one.
- Iteratively calculates probabilities for higher counts until the random number is matched.

This function is useful for generating synthetic data for testing or simulation studies involving one-inflated, zero-truncated negative binomial models.

Value

A numeric vector of simulated count data.

Examples

# Example usage
set.seed(123)
X <- matrix(rnorm(100), ncol = 2)
Z <- matrix(rnorm(100), ncol = 2)
b <- c(0.5, -0.2)
g <- c(1.0, 0.3)
alpha <- 1.5
simulated_data <- roiztnb(b, g, alpha, X, Z)
print(simulated_data)

# Example usage
set.seed(123)
X <- matrix(rnorm(100), ncol = 2)
Z <- matrix(rnorm(100), ncol = 2)
b <- c(0.5, -0.2)
g <- c(1.0, 0.3)
alpha <- 1.5
simulated_data <- roiztnb(b, g, alpha, X, Z)
print(simulated_data)

Generate Random Counts from a Zero-Truncated Poisson Process

Description

Simulates count data from a zero-truncated Poisson process using specified parameters for the rate component.

Usage

rpp(b, X)
rpp(b, X)

Arguments

`b`	A numeric vector of coefficients for the rate component.
`X`	A matrix or data frame of predictor variables for the rate component.

Details

This function generates count data from a zero-truncated Poisson process, which models count data without zeros. The process involves:

Calculating the rate parameter ( $\lambda$ ) as $\exp(X \cdot b)$ .
Iteratively computing probabilities for counts starting from 1 and adding to the cumulative probability until a randomly drawn value is matched.

This function is useful for generating synthetic data for testing or simulation studies involving zero-truncated Poisson models.

Value

A numeric vector of simulated count data.

Examples

# Example usage
set.seed(123)
X <- matrix(rnorm(100), ncol = 2)
b <- c(0.5, -0.2)
simulated_data <- rpp(b, X)
print(simulated_data)

# Example usage
set.seed(123)
X <- matrix(rnorm(100), ncol = 2)
b <- c(0.5, -0.2)
simulated_data <- rpp(b, X)
print(simulated_data)

Wald Test for Significance of a Predictor Variable

Description

Performs a Wald test to evaluate the joint significance of a predictor variable in both the rate and one-inflation components of a model.

Usage

signifWald(model, varname)
signifWald(model, varname)

Arguments

`model`	A fitted model object of class `"oneinflmodel"`.
`varname`	A character string specifying the name of the predictor variable to test.

Details

This function tests the null hypothesis that the coefficients for the specified predictor variable are jointly equal to zero in both the rate (beta) and one-inflation (gamma) components of the model. The test statistic is calculated as:

$W = \mathbf{c}^\top V^{-1} \mathbf{c}$

where $\mathbf{c}$ is the vector of coefficients for the predictor in the rate and one-inflation components, and $V$ is their variance-covariance matrix. The p-value is computed using a chi-squared distribution with 2 degrees of freedom.

Value

A list with the following components:

W: The Wald test statistic.
pval: The p-value associated with the test statistic, based on a chi-squared distribution with 2 degrees of freedom.

Examples

# Example usage
set.seed(123)
df <- data.frame(x = rnorm(100), z = rnorm(100), y = rpois(100, lambda = 5))
model <- oneinfl(y ~ x | z, df = df, dist = "Poisson")
result <- signifWald(model, varname = "x")
print(result$W)    # Wald test statistic
print(result$pval) # p-value

# Example usage
set.seed(123)
df <- data.frame(x = rnorm(100), z = rnorm(100), y = rpois(100, lambda = 5))
model <- oneinfl(y ~ x | z, df = df, dist = "Poisson")
result <- signifWald(model, varname = "x")
print(result$W)    # Wald test statistic
print(result$pval) # p-value

Summarize One-Inflated Regression Models

Description

Provides a summary of the fitted model, including estimated coefficients, standard errors, significance levels, and other relevant statistics.

Usage

## S3 method for class 'oneinflmodel'
summary(object, ...)
## S3 method for class 'oneinflmodel'
summary(object, ...)

Arguments

`object`	A model object of class `"oneinflmodel"` (for one-inflated models).
`...`	Additional arguments (currently unused).

Details

This function generates a detailed summary of the fitted model, including:

Estimated coefficients for the rate component (beta).
Estimated coefficients for the one-inflation component (gamma).
Standard errors.
z-statistics, associated p-values, and corresponding significance codes.
Average, and average absolute, one-inflation.
Log-likelihood of the fitted model.

Value

Prints a summary table of coefficients, standard errors, z-values, p-values, significance codes, one-inflation probabilities, and log-likelihood.

Examples

# Example usage
df <- data.frame(x = rnorm(100), z = rnorm(100), y = rpois(100, lambda = 5))
model <- oneinfl(y ~ x | z, df = df, dist = "Poisson")
summary(model)

# Example usage
df <- data.frame(x = rnorm(100), z = rnorm(100), y = rpois(100, lambda = 5))
model <- oneinfl(y ~ x | z, df = df, dist = "Poisson")
summary(model)

Summarize Truncated Regression Models

Description

Provides a summary of the fitted model, including estimated coefficients, standard errors, significance levels, and other relevant statistics.

Usage

## S3 method for class 'truncmodel'
summary(object, ...)
## S3 method for class 'truncmodel'
summary(object, ...)

Arguments

`object`	A model object of class `"truncmodel"` (for truncated models).
`...`	Additional arguments (currently unused).

Details

This function generates a detailed summary of the fitted model, including:

Estimated coefficients for the rate component (beta).
Standard errors.
z-statistics, associated p-values, and corresponding significance codes.
Log-likelihood of the fitted model.

Value

Prints a summary table of coefficients, standard errors, z-values, p-values, significance codes, and log-likelihood.

Examples

# Example usage
df <- data.frame(x = rnorm(100), y = rpois(100, lambda = 5))
model <- truncreg(y ~ x, df = df, dist = "Poisson")
summary(model)

# Example usage
df <- data.frame(x = rnorm(100), y = rpois(100, lambda = 5))
model <- truncreg(y ~ x, df = df, dist = "Poisson")
summary(model)

Truncated Regression Model

Description

Fits a positive Poisson (PP) or zero-truncated negative binomial (ZTNB) regression model.

Usage

truncreg(formula, df, dist = "negbin", start = NULL, method = "BFGS")
truncreg(formula, df, dist = "negbin", start = NULL, method = "BFGS")

Arguments

`formula`	A symbolic description of the model to be fitted.
`df`	A data frame containing the variables in the model.
`dist`	A character string specifying the distribution to use. Options are `"Poisson"` or `"negbin"`.
`start`	Optional. A numeric vector of starting values for the optimization process. Defaults to `NULL`, in which case starting values are attempted to be chosen automatically.
`method`	A character string specifying the optimization method to be passed to `optim`. Defaults to `"BFGS"`.

Details

This function fits a regression model for zero-truncated counts. Zero-truncated models are used when the count data does not include zeros, such as in cases where only positive counts are observed.

The function supports two distributions:

"Poisson": Zero-truncated Poisson regression.
"negbin": Zero-truncated negative binomial regression.

The function uses numerical optimization via optim to estimate the parameters.

Value

An object of class "truncmodel" containing the following components:

beta: Estimated coefficients for the regression model.
alpha: Dispersion parameter (only for negative binomial distribution).
vc: Variance-covariance matrix of the estimated parameters.
logl: Log-likelihood of the fitted model.
dist: The distribution used for the model ("Poisson" or "negbin").
formula: The formula used for the model.

Examples

# Example usage
df <- data.frame(x = rnorm(100), y = rpois(100, lambda = 1) + 1)
model <- truncreg(y ~ x, df = df, dist = "Poisson")
summary(model)

# Example usage
df <- data.frame(x = rnorm(100), y = rpois(100, lambda = 1) + 1)
model <- truncreg(y ~ x, df = df, dist = "Poisson")
summary(model)

Package 'oneinfl'

Help Index

Compute Marginal Effects for One-inflated models

Description

Usage

Arguments

Details

Value

See Also

Examples

One-Inflated Regression Model

Description

Usage

Arguments

Details

Value

See Also

Examples

Likelihood Ratio Test for Nested Models

Description

Usage

Arguments

Details

Value

See Also

Examples

Plot Observed Data and Model Predictions

Description

Usage

Arguments

Details

Value

See Also

Examples

Wald Test for One-Inflation

Description

Usage

Arguments

Details

Value

See Also

Examples

Predicted Expected Response for One-Inflated or Truncated Models

Description

Usage

Arguments

Details

Value

See Also

Examples

Predicted Expected Response for One-Inflated or Truncated Models

Description

Usage

Arguments

Details

Value

See Also

Examples

Generate Random Counts from a One-Inflated Poisson Process

Description

Usage

Arguments

Details

Value

See Also

Examples

Generate Random Counts from a One-Inflated Zero-Truncated Negative Binomial Process

Description

Usage

Arguments

Details

Value

See Also

Examples

Generate Random Counts from a Zero-Truncated Poisson Process

Description

Usage

Arguments

Details

Value