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, such that 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 for Guassian (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).

Link Description
1 Identity (residuals ~ Normal distribution)
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 either response (Y) or the explanatory input arrays.
  3. Number of maximum iteration input must be greater than one.
  4. The number of rows in response variable (Y) must be equal to number of rows of the explanatory variables (X).
  5. The betas input is optional, but if the user provide one, the number of betas must equal to the number of explanatory variables (i.e. X) plus one (intercept).
  6. For GLM with Poisson distribution,
    • The values of 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 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 Guassian distribution, the dispersion coefficient (Phi) must be either missing or a positive value.

Files Examples

References

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