GLM_CALIBRATE - GLM Parameters' Calibration

Computes the maximum likelihood estimate (MLE) of the model's parameters.

Syntax

GLM_CALIBRATE (Y, X, Betas, Phi, Lvk, MaxIter)

Y

is the dependent/response variable data set (a one-dimensional array of cells (e.g., rows or columns)). 

X

is the independent variables data matrix, so each column represents one variable.

Betas

are the initial values of the GLM coefficients (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).

Distribution	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).

MaxIter

is the maximum number of iterations used to calibrate the model. If missing, the default maximum of 100 is assumed.

Remarks

1. The underlying model is described here.
2. Missing values (i.e., #N/A!) are not allowed in the response (Y) or the explanatory input arrays.
3. The number of maximum iteration inputs must be greater than one.
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 value of the dispersion factor (Phi) must be either missing or equal to one.
7. For GLM with Binomial distribution,
   • The values of the response variable must be a non-negative fraction 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 coefficient (Phi) must be either missing or a positive value.

Files Examples

Related Links

• Wikipedia - Fisher information.
• Wikipedia - Generalized linear model.

References

• Hamilton, J.D.; Time Series Analysis, Princeton University Press (1994), ISBN 0-691-04289-6.
• Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740.