# GLM_RESID - GLM Residuals Time Series

Returns the standardized residuals/errors of a given GLM.

## Syntax

GLM_RESID (Y, X, Beta, Phi, Lvk)

Y
is the response or the dependent variable data array (a one-dimensional array of cells (e.g., rows or columns)).
X
is the independent variables data matrix, so each column represents one variable.
Beta
are the coefficients of the GLM model (a one-dimensional array of cells (e.g., rows or columns)).
Phi
is the GLM dispersion paramter. Phi is only meaningful for Binomial (1/batch or trial size) and Gaussian (variance).
Value Phi
Gaussian Variance.
Poisson 1.0.
Binomial Reciprocal of the batch/trial size).
Lvk
is the link function that describes how the mean depends on the linear predictor (1 = Identity (default), 2 = Log, 3 = Logit, 4 = Probit, 5 = Log-Log).
Value Lvk
1 Identity (Residuals ~ Normal distribution) (default).
2 Log (Residuals ~ Poisson distribution).
3 Logit (Residuals ~ Binomial distribution).
4 Probit (Residuals ~ Binomial distribution).
5 Complementary log-log (Residuals ~ Binomial distribution).

## Remarks

1. The underlying model is described here.
2. The GLM residuals are defined as follow: $$\left[\epsilon\right]= \left[Y\right] - g^{-1}(X\beta)$$
3. GLM_RESID returns an array of size equal to the number of rows in the input response (Y) or explanatory variables (X).
4. The number of rows in the response variable (Y) must equal the number of rows of the explanatory variables (X).
5. The betas input is optional, but if the user provides one, the number of betas must equal the number of explanatory variables (i.e., X) plus one (intercept).
6. For GLM with Poisson distribution,
• The values of the response variable must be non-negative integers.
• The dispersion factor (Phi) value must be missing or equal to one.
7. For GLM with Binomial distribution,
• The values of the response variable must be non-negative fractions between zero and one, inclusive.
• The value of the dispersion factor (Phi) must be a positive fraction (greater than zero and less than one).
8. For GLM with Gaussian distribution, the dispersion factor (Phi) value must be positive.