Supported Models¶

The zelig2 package supports 8 statistical models. The original Zelig package (Imai, King, and Lau 2007, 2008) supported many of the same model families; zelig2 retains the core set while adding fixed effects (via fixest, Bergé 2018), robust/clustered/bootstrap standard errors (via sandwich, Zeileis 2004), and seamless survey weight integration (via survey, Lumley 2004). All models support standard errors via robust, cluster, or bootstrap methods.

Model Summary¶

Model	String	Family	Link	Outcome Type	Fixed Effects	Survey Weights
Least Squares	`ls`	gaussian	identity	Continuous	Yes	Yes
Logistic Regression	`logit`	binomial	logit	Binary (0/1)	Yes	Yes
Probit Regression	`probit`	binomial	probit	Binary (0/1)	Yes	Yes
Poisson Regression	`poisson`	poisson	log	Count	Yes	Yes (quasipoisson)
Negative Binomial	`negbin`	custom	log	Overdispersed count	Yes	Yes (quasipoisson approx)
Gamma Regression	`gamma`	Gamma	inverse	Positive continuous	Yes	Yes
Tobit	`tobit`	custom	identity	Left-censored at 0	No	No
Quantile Regression	`quantile`	custom	identity	Conditional quantiles	No	No

Detailed Model Descriptions¶

Least Squares (OLS)¶

Model string: "ls"

Statistical specification: Gaussian family with identity link function

Use case: Linear regression for continuous, unbounded outcome variables.

Example formula:

zelig2(income ~ education + age, model = "ls", data = mydata)

Fixed effects: Supported via | syntax or fixef parameter

Survey weights: Supported via weights or full survey design specification

Logistic Regression¶

Model string: "logit"

Statistical specification: Binomial family with logit link function

Use case: Binary outcomes coded as 0/1. Estimates log-odds ratios.

Example formula:

zelig2(employed ~ education + age, model = "logit", data = mydata)

Fixed effects: Supported. Uses conditional fixed effects logit for panel data.

Survey weights: Supported via survey design or weights parameter

Note: Outcome must be binary (0/1). Use factor() for labeled categories if needed.

Probit Regression¶

Model string: "probit"

Statistical specification: Binomial family with probit (inverse normal) link function

Use case: Binary outcomes coded as 0/1. Assumes normally distributed latent variable.

Example formula:

zelig2(voted ~ income + education, model = "probit", data = mydata)

Fixed effects: Supported via within-transformation

Survey weights: Supported via survey design or weights parameter

Note: Similar to logit but uses normal CDF instead of logistic. Coefficients not directly comparable to logit.

Poisson Regression¶

Model string: "poisson"

Statistical specification: Poisson family with log link function

Use case: Count outcomes (non-negative integers). Assumes mean equals variance.

Example formula:

zelig2(num_arrests ~ age + income, model = "poisson", data = mydata)

Fixed effects: Supported via conditional maximum likelihood

Survey weights: Supported. Uses quasipoisson for survey designs to handle design effects.

Note: If outcome shows overdispersion (variance > mean), consider negative binomial model.

Negative Binomial¶

Model string: "negbin"

Statistical specification: Negative binomial distribution with log link

Use case: Overdispersed count data where variance exceeds the mean. More flexible than Poisson.

Example formula:

zelig2(hospital_visits ~ age + chronic_illness, model = "negbin", data = mydata)

Fixed effects: Supported via within-transformation

Survey weights: Supported. Uses quasipoisson approximation for survey designs.

Note: Includes dispersion parameter to model extra-Poisson variation.

Gamma Regression¶

Model string: "gamma"

Statistical specification: Gamma family with inverse link function

Use case: Positive continuous outcomes, often right-skewed (e.g., spending, duration, income).

Example formula:

zelig2(medical_spending ~ insurance + age, model = "gamma", data = mydata)

Fixed effects: Supported via within-transformation

Survey weights: Supported via survey design or weights parameter

Note: Outcome must be strictly positive (> 0). Appropriate for skewed positive data.

Tobit (Censored Regression)¶

Model string: "tobit"

Statistical specification: Normal distribution with left-censoring at 0

Use case: Continuous outcomes with a substantial proportion censored at zero (e.g., expenditures, time allocation).

Example formula:

zelig2(charity_donation ~ income + education, model = "tobit", data = mydata)

Fixed effects: NOT supported. Tobit models do not support fixed effects estimation.

Survey weights: NOT supported in current implementation

Implementation: Uses AER::tobit() for maximum likelihood estimation.

Note: Assumes latent variable is normally distributed. Zeros should represent true censoring, not structural zeros.

Quantile Regression¶

Model string: "quantile"

Statistical specification: Conditional quantile estimation via linear programming

Use case: Estimating effects at different points of the outcome distribution, not just the mean. Robust to outliers.

Example formula:

zelig2(income ~ education + age, model = "quantile", data = mydata)

Parameters: Specify tau for desired quantile (default 0.5 for median):

zelig2(income ~ education, model = "quantile", data = mydata, tau = 0.75)

Fixed effects: NOT supported. Quantile regression with fixed effects requires specialized methods.

Survey weights: NOT supported in current implementation

Implementation: Uses quantreg::rq() for estimation.

Note: Standard errors via bootstrap recommended. Useful when mean effects may be misleading due to heterogeneous treatment effects.

Choosing the Right Model¶

Continuous outcomes: - Unbounded, approximately normal: ls - Positive, right-skewed: gamma - Censored at zero: tobit - Quantile effects: quantile

Binary outcomes (0/1): - General use: logit - Latent variable interpretation: probit

Count outcomes: - No overdispersion: poisson - Overdispersion present: negbin

Need fixed effects? - Supported: ls, logit, probit, poisson, negbin, gamma - Not supported: tobit, quantile

Working with survey data? - Full support: ls, logit, probit, poisson, gamma - Approximation: negbin (uses quasipoisson) - Not supported: tobit, quantile