Heteroscedasticity-Consistent Covariance Matrix Estimation for singleRStaticCountData class

S3 method for vcovHC to handle singleRStaticCountData class objects. Works exactly like vcovHC.default the only difference being that this method handles vector generalised linear models. Updating the covariance matrix in variance/standard error estimation for population size estimator can be done via redoPopEstimation()

Usage

# S3 method for class 'singleRStaticCountData'
estfun(x, ...)

# S3 method for class 'singleRStaticCountData'
bread(x, ...)

# S3 method for class 'singleRStaticCountData'
vcovHC(
  x,
  type = c("HC3", "const", "HC", "HC0", "HC1", "HC2", "HC4", "HC4m", "HC5"),
  omega = NULL,
  sandwich = TRUE,
  ...
)

Arguments

x

a fitted singleRStaticCountData class object.

...

for vcovHC additional optional arguments passed to the following functions:

estfun – for empirical estimating functions.
hatvalues – for diagonal elements of projection matrix.
sandwich – only if sandwich argument in function call was set to TRUE.
vcov – when calling bread internally.

type

a character string specifying the estimation type, same as in sandwich::vcovHC.default. HC3 is the default value.

omega

a vector or a function depending on the arguments residuals (i.e. the derivative of log-likelihood with respect to each linear predictor), diaghat (the diagonal of the corresponding hat matrix) and df (the residual degrees of freedom), same as in sandwich::vcovHC.default.

sandwich

logical. Should the sandwich estimator be computed? If set to FALSE only the meat matrix is returned. Same as in sandwich::vcovHC()

Value

Variance-covariance matrix estimation corrected for heteroscedasticity of regression errors.

Author

Piotr Chlebicki, Maciej Beręsewicz

Examples

set.seed(1)
N <- 10000
gender <- rbinom(N, 1, 0.2)
eta <- -1 + 0.5*gender
counts <- rpois(N, lambda = exp(eta))
df <- data.frame(gender, eta, counts)
df2 <- subset(df, counts > 0)
mod1 <-  estimatePopsize(
  formula = counts ~ 1 + gender, 
  data = df2, 
  model = "ztpoisson", 
  method = "optim", 
  popVar = "analytic"
)
require(sandwich)
HC <- sandwich::vcovHC(mod1, type = "HC4")
Fisher <- vcov(mod1, "Fisher") # variance covariance matrix obtained from 
#Fisher (expected) information matrix
HC
#>             (Intercept)       gender
#> (Intercept)  0.00201216 -0.002012160
#> gender      -0.00201216  0.004790297
Fisher
#>              (Intercept)       gender
#> (Intercept)  0.002022145 -0.002022145
#> gender      -0.002022145  0.004881858
# usual results
summary(mod1)
#> 
#> Call:
#> estimatePopsize.default(formula = counts ~ 1 + gender, data = df2, 
#>     model = "ztpoisson", method = "optim", popVar = "analytic")
#> 
#> Pearson Residuals:
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#> -0.5503 -0.4267 -0.4267  0.0000 -0.4267  6.2261 
#> 
#> Coefficients:
#> -----------------------
#> For linear predictors associated with: lambda 
#>             Estimate Std. Error z value  P(>|z|)    
#> (Intercept) -1.01346    0.04497 -22.537  < 2e-16 ***
#> gender       0.50288    0.06987   7.197 6.14e-13 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> AIC: 3990.538
#> BIC: 4002.804
#> Residual deviance: 2386.29
#> 
#> Log-likelihood: -1993.269 on 3403 Degrees of freedom 
#> Number of calls to log-likelihood function: 35
#> -----------------------
#> Population size estimation results: 
#> Point estimate 10146.02
#> Observed proportion: 33.6% (N obs = 3405)
#> Std. Error 341.7287
#> 95% CI for the population size:
#>           lowerBound upperBound
#> normal      9476.239   10815.79
#> logNormal   9508.827   10849.72
#> 95% CI for the share of observed population:
#>           lowerBound upperBound
#> normal      31.48175   35.93198
#> logNormal   31.38330   35.80883
# updated results
summary(mod1, cov = HC,
popSizeEst = redoPopEstimation(mod1, cov = HC))
#> 
#> Call:
#> estimatePopsize.default(formula = counts ~ 1 + gender, data = df2, 
#>     model = "ztpoisson", method = "optim", popVar = "analytic")
#> 
#> Pearson Residuals:
#>    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
#> -0.5503 -0.4267 -0.4267  0.0000 -0.4267  6.2261 
#> 
#> Coefficients:
#> -----------------------
#> For linear predictors associated with: lambda 
#>             Estimate Std. Error z value  P(>|z|)    
#> (Intercept) -1.01346    0.04486 -22.593  < 2e-16 ***
#> gender       0.50288    0.06921   7.266 3.71e-13 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> AIC: 3990.538
#> BIC: 4002.804
#> Residual deviance: 2386.29
#> 
#> Log-likelihood: -1993.269 on 3403 Degrees of freedom 
#> Number of calls to log-likelihood function: 35
#> -----------------------
#> Population size estimation results: 
#> Point estimate 10146.02
#> Observed proportion: 33.6% (N obs = 3405)
#> Std. Error 340.7902
#> 95% CI for the population size:
#>           lowerBound upperBound
#> normal      9478.078   10813.95
#> logNormal   9510.489   10847.69
#> 95% CI for the share of observed population:
#>           lowerBound upperBound
#> normal      31.48710   35.92500
#> logNormal   31.38916   35.80257
# estimating equations
mod1_sims <- sandwich::estfun(mod1)
head(mod1_sims)
#>   (Intercept)    gender
#> 1  -0.1924342 0.0000000
#> 2   0.6700925 0.6700925
#> 3  -0.1924342 0.0000000
#> 4  -0.1924342 0.0000000
#> 5  -0.1924342 0.0000000
#> 6  -0.1924342 0.0000000
# bread method
all(vcov(mod1, "Fisher") * nrow(df2) == sandwich::bread(mod1, type = "Fisher"))
#> [1] TRUE

Usage

Arguments

Value

See also

Author

Examples