` erfe `

packageThe ` erfe `

package estimates the expectile regression panel
fixed effect model (**ERFE**). The **ERFE** model is a expectile-based
method for panel data. The **ERFE** model extends the within
transformation strategy to solve the incidental parameter problem within
the expectile regression framework. The **ERFE** model estimates the
regressor effects on the expectiles of the response distribution. The
**ERFE** model captures the data heteroscedasticity and eliminates any
bias resulting from the correlation between the regressors and the
omitted factors. When $\tau=0.5$ the ERFE model estimator corresponds to
the classical fixed-effects within estimator.

` erfe `

packageThe main function of the ` erfe `

package is the ```
erfe
```

function and consists of four arguments. The ```
predictors
```

matrix which corresponds to the design matrix or the matrix of
regressors. Note that, the design matrix should contain time varying
regressors only, because the **ERFE** model do not make inference for
time-invariant regressors. The ` response `

variable is the
continuous response variable, and the ` asymp `

parameter
corresponds to the vector of asymmetric points with default values:
$\tau \in (0.25, \ 0.5, \ 0.75).$ The ` id `

parameter
corresponds to the subject ids and should be ordered according to the
time or year.

You can install the development version of the ` erfe `

package from GitHub with:

```
# install.packages("devtools")
devtools::install_github("amadoudiogobarry/erfe")
```

This is a basic example which shows you how to use the main function of the package:

```
library(erfe)
data(sim_panel_data) # Toy dataset
head(sim_panel_data)
#> id pred1 pred2 resp nobs year
#> 1 1 1.9367572 2.386914 4.943895 50 1
#> 2 1 0.1368550 3.731007 4.584137 50 2
#> 3 1 5.8850632 3.600262 8.405295 50 3
#> 4 1 2.5455661 3.416180 6.011400 50 4
#> 5 1 -0.3971390 5.367943 6.237594 50 5
#> 6 2 -0.2610938 -1.326893 -3.258152 50 1
asymp <- c(0.25,0.5,0.75) # sequence of asymmetric points
predictors <- as.matrix(cbind(sim_panel_data$pred1, sim_panel_data$pred2)) # design matrix
response <- sim_panel_data$resp # response variable
id <- sim_panel_data$id # ordered subject ids variable
outlist <- erfe(predictors, response, asymp=c(0.25,0.5,0.75), id)
```

For each asymmetric point, we have a list of results including the
asymmetric point itself, the estimator and the estimator of its
covariance matrix, and the residuals of the model. For example, the
results of the **ERFE** model for $\tau=0.75$ can be retrieved like
this:

```
outlist75 <- outlist[[3]]
# coef estimate
outlist75$coefEst
#> X1 X2
#> 0.5995653 0.9585377
# covariance estimate
outlist75$covMat
#> 2 x 2 Matrix of class "dgeMatrix"
#> [,1] [,2]
#> [1,] 0.04042441 0.1457498
#> [2,] 0.14574977 0.6555698
```

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