bife (version 0.5)

bife: Binary Choice Models with Fixed Effects

Description

bife is used to fit fixed effects binary choice models (logit and probit) based on an unconditional likelihood approach. It is tailored for the fast estimation of binary choice models with potentially many individual fixed effects. The large dummy variable matrix is avoided by a special iteratively reweighted least squares demeaning algorithm (Stammann, Heiss, and McFadden, 2016). The incidental parameter bias occuring in panels with shorter time horizons can be reduced by analytical bias-correction (Newey and Hahn, 2004). If no bias-correction is applied, the estimated coefficients will be identical to the ones obtained by glm. However, bife will compute faster than glm, if the model exhibits many fixed effects.

Remark: The term fixed effect is used in econometrician`s sense of having a time-constant dummy for each individual. All other parameters in the model are referred to as structural parameters.

Usage

bife(formula, data = list(), beta_start = NULL, model = "logit",
  bias_corr = "ana", iter_demeaning = 100L, tol_demeaning = 1e-05,
  iter_offset = 1000L, tol_offset = 1e-05)

Arguments

formula

an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted. formula must be of type \(y ~ x | id\) where the id refers to an individual identifier (fixed effects).

data

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

beta_start

an optional vector of starting values used for the structural parameters in the demeaning algorithm. Default is zero for all structural parameters.

model

the description of the error distribution and link function to be used in the model. For bife this has to be a character string naming the model function. The value should be any of "logit" or "probit". Default is "logit".

bias_corr

an optional string that specifies the type of the bias-correction: no bias-correction or analytical. The value should be any of "no" or "ana". Default is "ana" (analytical).

iter_demeaning

an optional integer value that specifies the maximum number of iterations of the demeaning algorithm. Default is 100. Details are given under Details.

tol_demeaning

an optional number that specifies the tolerance level of the demeaning algorithm. Default is 1e-5. Details are given under Details.

iter_offset

an optional integer value that specifies the maximum number of iterations of the offset algorithm for the computation of bias-adjusted fixed effects. Default is 1000. Details are given under Details.

tol_offset

an optional number that specifies the tolerance level of the offset algorithm for the computation of bias-adjusted fixed effects. Default is 1e-5. Details are given under Details.

Value

An object of class bife is a list containing the following components:

par

$beta

a vector of the uncorrected structural parameters

$alpha

a vector of the uncorrected fixed effects

$se_beta

a vector of the standard errors of the uncorrected structural parameters

$se_alpha

a vector of the standard errors of the uncorrected fixed effects

$beta_vcov

a matrix of the covariance matrix of the uncorrected structural parameters

$avg_alpha

the average of the uncorrected fixed effects

par_corr

$beta

a vector of the bias-corrected structural parameters

$alpha

a vector of the bias-adjusted fixed effects

$se_beta

a vector of the standard errors of the bias-corrected structural parameters

$se_alpha

a vector of the standard errors of the bias-adjusted fixed effects

$beta_vcov

a matrix of the covariance matrix of the bias-corrected structural parameters

$avg_alpha

the average of the bias-adjusted fixed effects

logl_info

$nobs

number of observations

$k

number of loglikelihood parameters

$loglik

the log likelihood value given the uncorrected parameters

$events

number of events

$iter_demeaning

the number of iterations of the demeaning algorithm

$conv_demeaning

a logical value indicating convergence of the demeaning algorithm

$loklik_corr

the log likelihood given the bias-corrected/-adjusted parameters

$iter_offset

the number of iterations of the offset algorithm

$conv_offset

a logical value indicating convergence of the offset algorithm

model_info

$used_ids

a vector of the retained ids during fitting

$y

the response vector given $used.ids

$beta_start

a vector of used starting values

$X

the model matrix given $used.ids

$id

a vector of the individual identifier given $used.ids

$t

a vector of the time identifier given $used.ids

$drop_pc

number of individuals dropped during fitting due to non-varying response (perfect classification)

$drop_NA

number of individuals dropped due to missing values

...

further objects passed to other methods in bife

Details

A typical predictor has the form \(response ~ terms | id\) where response is the binary response vector (0-1 coded), terms is a series of terms which specifies a linear predictor for the response, and refers to an individual identifier. The linear predictor must not include any constant regressors due to the perfect collinearity with the fixed effects. Since individuals with a non-varying response do not contribute to the log likelihood they are dropped from the estimation procedure (unlike glm). The analytical bias-correction follows Newey and Hahn (2004).

Details for iter_demeaning and tol_demeaning: A special iteratively reweighted least squares demeaning algorithm is used following Stammann, A., F. Heiss, and D. McFadden (2016). The stopping criterion is defined as \(||b(i) - b(i - 1)|| < tol_demeaning\).

Details for iter_offset and tol_offset: The bias-adjusted fixed effects are computed via an iteratively reweighted least (IWLS) squares algorithm efficiently tailored to sparse data. The algorithm includes the bias-corrected structural parameters in the linear predictor during fitting. The stopping criterion in the IWLS algorithm is defined as \(any(|b(i) - b(i - 1)| / |b(i - 1)|) < tol_offset\).

References

Hahn, J., and W. Newey (2004). "Jackknife and analytical bias reduction for nonlinear panel models". Econometrica 72(4), 1295-1319.

Stammann, A., F. Heiss, and D. McFadden (2016). "Estimating Fixed Effects Logit Models with Large Panel Data". Working paper.

Examples

# NOT RUN {
library("bife")

# Load 'psid' dataset
dataset <- psid
head(dataset)

# Fixed effects logit model w/o bias-correction
mod_no <- bife(LFP ~ AGE + I(INCH / 1000) + KID1 + KID2 + KID3 | ID, 
 data = dataset, bias_corr = "no")

# Summary of uncorrected structural parameters only        
summary(mod_no)

# Summary plus fixed effects
summary(mod_no, fixed = TRUE)

# Fixed effects logit model with analytical bias-correction
mod_ana <- bife(LFP ~ AGE + I(INCH / 1000) + KID1 + KID2 + KID3 | ID,
 data = dataset)
               
# Summary of bias-corrected structural parameters only
summary(mod_ana)

# Summary of uncorrected structural parameters only
summary(mod_ana, corrected = FALSE)

# Summary of bias-corrected structural parameters plus -adjusted
# fixed effects
summary(mod_ana, fixed = TRUE)

# Extract bias-corrected structural parameters of mod_ana
beta_ana <- coef(mod_ana)
print(beta_ana)

# Extract bias-adjusted fixed effects of mod_ana
alpha_ana <- coef(mod_ana, fixed = TRUE)
print(alpha_ana)

# Extract uncorrected structural parameters of mod_ana
beta_no <- coef(mod_ana, corrected = FALSE)
print(beta_no)

# Extract covariance matrix of bias-corrected structural
# parameters of mod_ana
vcov_ana <- vcov(mod_ana)
print(vcov_ana)

# Extract covariance matrix of uncorrected structural parameters
# of mod_ana
vcov_no <- vcov(mod_ana, corrected = FALSE)
print(vcov_no)

# }