Package 'oneinfl'

Prepare Design Matrices and Response Vector

Description

Processes a model formula and a data frame to generate design matrices ('X' and 'Z') and a response vector ('y') for regression models, including support for complex formulas with '|' operators.

Usage

makeXZy(formula, df)

Arguments

formula	A symbolic description of the model, where the left-hand side specifies the response variable and the right-hand side specifies predictors. Formulas can include a '|' operator to separate predictors for different components of a model.
df	A data frame containing the variables specified in the formula.

Details

This function processes the formula to extract and construct: - 'X': The main design matrix. - 'Z': A secondary design matrix (if a '|' operator is used in the formula, separating components). - 'y': The response variable.

It handles cases where the formula specifies: - Only the main component (e.g., y ~ x1 + x2). - A secondary component using the '|' operator (e.g., y ~ x1 + x2 | z1 + z2).

Value

A list containing the following components:

X

A design matrix for the main predictors.

Z

A design matrix for additional predictors (e.g., for a secondary process in a two-component model).

y

The response vector extracted from the formula.

See Also

model.matrix, model.frame, model.response

---

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", verbose = TRUE)

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.
verbose	Logical; if TRUE (default), prints the summary output. If FALSE, suppresses output table and returns a list containing several components.

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

If verbose=TRUE (default), prints the marginal effects, their standard errors, z-values, p-values, and significance levels.

If verbose=FALSE, returns a list containing the following components:

where

A description of how the marginal effects have been evaluated.

dEdq

The marginal effect. The partial derivative of the expected count with respect to a variable q in the X and or Z matrix, or the difference in expectation if q is binary.

se

The standard errors of the marginal effects evaluated numerically and using a Jacobian via the delta method.

See Also

dEdq_nb, dEdq_nb_noinfl, dEdq_pois, dEdq_pois_noinfl, model.frame, model.matrix, numericDeriv

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", verbose=FALSE) # Effect at Means, suppress printing
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")

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.

See Also

summary for summarizing the fitted model. margins for calculating the marginal effects of regressors. oneWald to test for no one-inflation. signifWald for testing the joint significance of a single regressor that appears before and after the pipe '|'. oneplot for plotting actual and predicted counts. predict for expected response/dependent variable at each observation. truncreg for fitting positive Poisson (PP) and zero-truncated negative binomial (ZTNB) models. oneLRT to test for no one-inflation or no overdispersion using a nested PP, OIPP, or ZTNB 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=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)

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.

See Also

oneinfl for fitting one-inflated models. truncreg for fitting zero-truncated models. pchisq for the 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)

---

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 = NULL,
  model3 = NULL,
  model4 = NULL,
  df,
  maxpred = NULL,
  ylimit = NULL,
  ccex = 1.5
)

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.
model4	Optional. A fourth fitted model object.
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.

See Also

oneinfl for fitting one-inflated models. truncreg for fitting truncated models. pred for generating predictions used in the plot.

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 = "Poisson")
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)

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.

See Also

oneinfl for fitting one-inflated models. oneLRT for a likelihood ratio test of nested models. pchisq for the 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)

---

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(object, ...)

Arguments

object	An object of class 'oneinflmodel'
...	Additional argument 'df', a data frame used to calculate 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.

See Also

oneinfl for fitting one-inflated models. E_pois, E_negbin, for the expected value calculations.

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)

---

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(object, ...)

Arguments

object	An object of class 'truncmodel'
...	Additional argument 'df', a data frame used to calculate 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.

See Also

oneinfl for fitting one-inflated models. truncreg for fitting truncated models. E_pois_noinfl, E_negbin_noinfl for the expected value calculations.

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)

---

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)

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:

1. Calculates the rate parameter ($\lambda$) as $\exp(X \cdot b)$.

2. Computes the one-inflation probabilities ($\omega$) based on $Z \cdot g$.

3. 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.

See Also

oneinfl for fitting one-inflated models.

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)

---

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)

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:

1. Calculates the rate parameter ($\lambda$) as $\exp(X \cdot b)$.

2. Computes the one-inflation probabilities ($\omega$) based on $Z \cdot g$.

3. Computes the negative binomial dispersion parameter ($\theta = \lambda / \alpha$).

4. 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.

See Also

oneinfl for fitting one-inflated models.

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)

---

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)

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.

See Also

truncreg for fitting zero-truncated models.

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)

---

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)

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.

See Also

oneinfl for fitting one-inflated models. oneWald for a general Wald test of one-inflation parameters.

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

---

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, ...)

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.

See Also

oneinfl for fitting one-inflated models.

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)

---

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, ...)

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.

See Also

truncreg for fitting truncated regression models.

Examples

# 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")

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.

See Also

summary for summarizing the fitted 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)

---