library("MASS")
library("stargazer")
Please cite as: Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables. R package version 5.2.3. https://CRAN.R-project.org/package=stargazer library("car") Loading required package: carDataset.seed(123)df <- mtcarsIf you run into modelling issues, try to -
Relax the convergence criterion (epsilon = 1e-4) - keep it less than 0 though.
Check for collinearity (VIF) and remove highly correlated predictors.
Inspect data for extreme values and handle them appropriately.
Use Poisson regression to generate better starting values.
Simplify the model by removing less relevant predictors.
?distributions
model1 <- glm.nb( formula = carb ~ mpg + cyl + wt +qsec +vs +am,
data = df
)Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
control$trace > : iteration limit reached
Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
control$trace > : iteration limit reachedmodel2 <- glm.nb( formula = carb ~ mpg + cyl + wt +qsec +vs +am,
data = df,
control = glm.control(maxit = 1000, # keep uptil 1000
epsilon = 1e-6, # keep between 1e-8 and 1e-1
trace = TRUE # Enable debugging to track what happens during the optimization process
)
)Warning in sqrt(1/i): NaNs producedWarning in sqrt(1/i): NaNs producedTheta(1) = 4304520000000.000000, 2(Ls - Lm) = 9.343750stargazer(model1, model2,
type = "text"
)
===================================================================
Dependent variable:
-------------------------------------------------
carb
(1) (2)
-------------------------------------------------------------------
mpg -0.038 -0.038
(0.053) (0.053)
cyl -0.106 -0.106
(0.198) (0.198)
wt 0.258 0.258
(0.271) (0.271)
qsec -0.213 -0.213
(0.158) (0.158)
vs 0.093 0.093
(0.464) (0.464)
am 0.255 0.255
(0.422) (0.422)
Constant 5.191 5.191
(3.523) (3.523)
-------------------------------------------------------------------
Observations 32 32
Log Likelihood -50.206 -50.031
theta 132,293.200 (3,255,983.000) 4,304,518,627,158.000
Akaike Inf. Crit. 114.413 114.062
===================================================================
Note: *p<0.1; **p<0.05; ***p<0.01If convergence fails, try to increase the maxit (maxium iterations), and increase the error (relax the epsilon constraint by increasing its magnitude).
A very high value of Theta (dispersion parameter - controls the variance of negative binomial distribution) implies that the variance is approaching the variance of a Poisson distribution, suggesting that overdispersion is minimal or that the optimization algorithm is struggling to fit Theta correctly.
hist(df$carb)
var(df$carb)/mean(df$carb)[1] 0.9275986Either way, look at the output.
boxplot(df) 
3 * IQR is a good rule of thumb.
vif(glm(carb ~ mpg + cyl + wt + qsec + vs + am, data = df)) mpg cyl wt qsec vs am
6.721984 9.710670 6.483070 5.585198 4.502740 4.042162 Not an issue here, and thus no variables have to be removed.
poisson_model <- glm(carb ~ mpg + cyl + wt + qsec + vs + am, family = poisson, data = df)model3 <- glm.nb( formula = carb ~ mpg + cyl + wt + qsec + vs + am,
data = df,
start = coef(poisson_model)
)Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
control$trace > : iteration limit reached
Warning in theta.ml(Y, mu, sum(w), w, limit = control$maxit, trace =
control$trace > : iteration limit reachedmodel4 <- glm.nb( formula = carb ~ mpg + cyl + wt + qsec + vs + am,
data = df,
start = coef(poisson_model),
control = glm.control(maxit = 300, # keep uptil 1000
epsilon = 1e-8, # keep between 1e-8 and 1e-1
trace = TRUE # Enable debugging to track what happens
)
)Warning in sqrt(1/i): NaNs produced
Warning in sqrt(1/i): NaNs producedTheta(1) = 124691000.000000, 2(Ls - Lm) = 9.046400If the model includes too many predictors relative to the number of observations, it may be overparameterized. Consider simplifying the model by removing less important predictors.
stargazer(model1, model2, model3, model4,
type = "text")
===============================================================================================================
Dependent variable:
---------------------------------------------------------------------------------------------
carb
(1) (2) (3) (4)
---------------------------------------------------------------------------------------------------------------
mpg -0.038 -0.038 -0.038 -0.038
(0.053) (0.053) (0.053) (0.053)
cyl -0.106 -0.106 -0.106 -0.106
(0.198) (0.198) (0.198) (0.198)
wt 0.258 0.258 0.258 0.258
(0.271) (0.271) (0.271) (0.271)
qsec -0.213 -0.213 -0.213 -0.213
(0.158) (0.158) (0.158) (0.158)
vs 0.093 0.093 0.093 0.093
(0.464) (0.464) (0.464) (0.464)
am 0.255 0.255 0.255 0.255
(0.422) (0.422) (0.422) (0.422)
Constant 5.191 5.191 5.191 5.191
(3.523) (3.523) (3.523) (3.523)
---------------------------------------------------------------------------------------------------------------
Observations 32 32 32 32
Log Likelihood -50.206 -50.031 -50.206 -50.206
theta 132,293.200 (3,255,983.000) 4,304,518,627,158.000 132,293.700 (3,255,978.000) 124,690,658.000
Akaike Inf. Crit. 114.413 114.062 114.413 114.412
===============================================================================================================
Note: *p<0.1; **p<0.05; ***p<0.01