In some occasions, the optimization algorithm of `femlm`

may fail to converge, or
the variance-covariance matrix may not be available. The most common reason of why
this happens is collinearity among variables. This function helps to find out which
set of variables is problematic.

## Details

This function tests: 1) collinearity with the fixed-effect variables, 2) perfect multi-collinearity between the variables, 3) perfect multi-collinearity between several variables and the fixed-effects, and 4) identification issues when there are non-linear in parameters parts.

## Examples

```
# Creating an example data base:
set.seed(1)
fe_1 = sample(3, 100, TRUE)
fe_2 = sample(20, 100, TRUE)
x = rnorm(100, fe_1)**2
y = rnorm(100, fe_2)**2
z = rnorm(100, 3)**2
dep = rpois(100, x*y*z)
base = data.frame(fe_1, fe_2, x, y, z, dep)
# creating collinearity problems:
base$v1 = base$v2 = base$v3 = base$v4 = 0
base$v1[base$fe_1 == 1] = 1
base$v2[base$fe_1 == 2] = 1
base$v3[base$fe_1 == 3] = 1
base$v4[base$fe_2 == 1] = 1
# Estimations:
# Collinearity with the fixed-effects:
res_1 = femlm(dep ~ log(x) + v1 + v2 + v4 | fe_1 + fe_2, base)
#> Warning: [femlm]: The optimization algorithm did not converge, the results are not reliable. The information matrix is singular: presence of collinearity.
collinearity(res_1)
#> [1] "Variables 'v1' and 'v2' are collinear with fixed-effects `fe_1`."
# => collinearity with the first fixed-effect identified, we drop v1 and v2
res_1bis = femlm(dep ~ log(x) + v4 | fe_1 + fe_2, base)
#> Warning: [femlm]: The information matrix is singular: presence of collinearity.
collinearity(res_1bis)
#> [1] "Variable 'v4' is collinear with fixed-effects `fe_2`."
# Multi-Collinearity:
res_2 = femlm(dep ~ log(x) + v1 + v2 + v3 + v4, base)
#> Warning: [femlm]: The optimization algorithm did not converge, the results are not reliable. The information matrix is singular: presence of collinearity.
collinearity(res_2)
#> [1] "Variable `v1` is collinear with variables '(Intercept)', 'v2' and 'v3'."
```