Specifies the information required to fit a Beta, zero-inflated and hurdle Poisson, zero-inflated and hurdle Negative Binomial, a hurdle normal and a hurdle Beta mixed-effects model, using mixed_model().

students.t(df = stop("'df' must be specified"), link = "identity")
beta.fam()
zi.poisson()
zi.binomial()
zi.negative.binomial()
hurdle.poisson()
hurdle.negative.binomial()
hurdle.lognormal()
hurdle.beta.fam()
unit.lindley()
Gamma.fam()
censored.normal()

## Arguments

df

the degrees of freedom of the Student's t distribution.

## Note

Currently only the log-link is implemented for the Poisson, negative binomial and Gamma models, the logit link for the beta and hurdle beta models and the identity link for the log-normal model.

## Examples

# simulate some data from a negative binomial model
set.seed(102)
dd <- expand.grid(f1 = factor(1:3), f2 = LETTERS[1:2], g = 1:30, rep = 1:15,
KEEP.OUT.ATTRS = FALSE)
mu <- 5*(-4 + with(dd, as.integer(f1) + 4 * as.numeric(f2)))
dd\$y <- rnbinom(nrow(dd), mu = mu, size = 0.5)

# Fit a zero-inflated Poisson model, with only fixed effects in the
# zero-inflated part
fm1 <- mixed_model(fixed = y ~ f1 * f2, random = ~ 1 | g, data = dd,
family = zi.poisson(), zi_fixed = ~ 1)

summary(fm1)
#>
#> Call:
#> mixed_model(fixed = y ~ f1 * f2, random = ~1 | g, data = dd,
#>     family = zi.poisson(), zi_fixed = ~1)
#>
#> Data Descriptives:
#> Number of Observations: 2700
#> Number of Groups: 30
#>
#> Model:
#>  family: zero-inflated poisson
#>
#> Fit statistics:
#>    log.Lik      AIC      BIC
#>  -38656.66 77329.32 77340.53
#>
#> Random effects covariance matrix:
#>                StdDev
#> (Intercept) 0.1206881
#>
#> Fixed effects:
#>             Estimate Std.Err  z-value p-value
#> (Intercept)   2.0369  0.0301  67.7765 < 1e-04
#> f12           0.5228  0.0253  20.6624 < 1e-04
#> f13           0.9018  0.0239  37.7840 < 1e-04
#> f2B           1.3992  0.0224  62.5730 < 1e-04
#> f12:f2B      -0.3802  0.0282 -13.4937 < 1e-04
#> f13:f2B      -0.6665  0.0268 -24.9152 < 1e-04
#>
#> Zero-part coefficients:
#>             Estimate Std.Err  z-value p-value
#> (Intercept)  -1.4413  0.0489 -29.4463 < 1e-04
#>
#> Integration:
#>
#> Optimization:
#> method: hybrid EM and quasi-Newton
#> converged: TRUE

# \donttest{
# We extend the previous model allowing also for a random intercept in the
# zero-inflated part
fm2 <- mixed_model(fixed = y ~ f1 * f2, random = ~ 1 | g, data = dd,
family = zi.poisson(), zi_fixed = ~ 1, zi_random = ~ 1 | g)

# We do a likelihood ratio test between the two models
anova(fm1, fm2)
#>
#>          AIC      BIC   log.Lik  LRT df p.value
#> fm1 77329.32 77340.53 -38656.66
#> fm2 77331.95 77345.96 -38655.97 1.37  2  0.5047
#>

#############################################################################
#############################################################################

# The same as above but with a negative binomial model
gm1 <- mixed_model(fixed = y ~ f1 * f2, random = ~ 1 | g, data = dd,
family = zi.negative.binomial(), zi_fixed = ~ 1)

summary(gm1)
#>
#> Call:
#> mixed_model(fixed = y ~ f1 * f2, random = ~1 | g, data = dd,
#>     family = zi.negative.binomial(), zi_fixed = ~1)
#>
#> Data Descriptives:
#> Number of Observations: 2700
#> Number of Groups: 30
#>
#> Model:
#>  family: zero-inflated negative binomial
#>
#> Fit statistics:
#>    log.Lik     AIC      BIC
#>  -10031.15 20080.3 20092.91
#>
#> Random effects covariance matrix:
#>                 StdDev
#> (Intercept) 0.04718218
#>
#> Fixed effects:
#>             Estimate Std.Err z-value    p-value
#> (Intercept)   1.6877  0.0738 22.8762    < 1e-04
#> f12           0.6210  0.0994  6.2470    < 1e-04
#> f13           1.0012  0.0992 10.0975    < 1e-04
#> f2B           1.6138  0.0987 16.3563    < 1e-04
#> f12:f2B      -0.4724  0.1388 -3.4028 0.00066693
#> f13:f2B      -0.7344  0.1386 -5.2979    < 1e-04
#>
#> Zero-part coefficients:
#>             Estimate Std.Err z-value  p-value
#> (Intercept)  -5.0279   2.785 -1.8053 0.071024
#>
#> log(dispersion) parameter:
#>   Estimate Std.Err
#>    -0.7205  0.0545
#>
#> Integration:
#>
#> Optimization:
#> method: hybrid EM and quasi-Newton
#> converged: TRUE

# We do a likelihood ratio test between the Poisson and negative binomial models
anova(fm1, gm1)
#>
#>          AIC      BIC   log.Lik      LRT df p.value
#> fm1 77329.32 77340.53 -38656.66
#> gm1 20080.30 20092.91 -10031.15 57251.01  1 <0.0001
#>
# }