NAG C Library Function Document

nag_glm_tran_model (g02gkc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{ip}$ – IntegerInput

On entry: the number of terms in the linear model, $p$.

Constraint: $\mathbf{ip}\ge 1$.

2:    $\mathbf{nclin}$ – IntegerInput

On entry: the number of constraints to be imposed on the arguments, $n_c$.

Constraint: $0<\mathbf{nclin}<\mathbf{ip}$.

3:    $\mathbf{v}\left[\mathbf{ip}\times \mathbf{tdv}\right]$ – const doubleInput

Note: the $\left(i,j\right)$th element of the matrix $V$ is stored in $\mathbf{v}\left[\left(i-1\right)\times \mathbf{tdv}+j-1\right]$.

On entry: v as returned by nag_glm_normal (g02gac), nag_glm_binomial (g02gbc), nag_glm_poisson (g02gcc) or nag_glm_gamma (g02gdc).

4:    $\mathbf{tdv}$ – IntegerInput

On entry: the stride separating matrix column elements in the array v.

Constraint: $\mathbf{tdv}\ge \mathbf{ip}+6$.

tdv should be as supplied to nag_glm_normal (g02gac), nag_glm_binomial (g02gbc), nag_glm_poisson (g02gcc) or nag_glm_gamma (g02gdc).

5:    $\mathbf{c}\left[\mathbf{ip}\times \mathbf{tdc}\right]$ – const doubleInput

Note: the $\left(i,j\right)$th element of the matrix $C$ is stored in $\mathbf{c}\left[\left(i-1\right)\times \mathbf{tdc}+j-1\right]$.

On entry: the nclin constraints stored by column, i.e., the $i$th constraint is stored in the $i$th column of c.

6:    $\mathbf{tdc}$ – IntegerInput

On entry: the stride separating matrix column elements in the array c.

Constraint: $\mathbf{tdc}\ge \mathbf{nclin}$.

7:    $\mathbf{b}\left[\mathbf{ip}\right]$ – doubleInput/Output

On entry: the parameter estimates computed by using the singular value decomposition, ${\hat{\beta }}_{svd}$.

On exit: the parameter estimates of the arguments with the constraints imposed, ${\hat{\beta }}_c$.

8:    $\mathbf{scale}$ – doubleInput

On entry: the estimate of the scale argument.

For results from nag_glm_normal (g02gac) and nag_glm_gamma (g02gdc) then scale is the scale argument, for the model ${\sigma }^2$ and ${\hat{\nu }}^{-1}$ respectively.

For results from nag_glm_binomial (g02gbc) and nag_glm_poisson (g02gcc) then scale should be set to 1.0.

Constraint: $\mathbf{scale}>0.0$.

9:    $\mathbf{se}\left[\mathbf{ip}\right]$ – doubleOutput

On exit: the standard error of the parameter estimates in b.

10:  $\mathbf{cov}\left[\left(\mathbf{ip}\right)\times \left(\mathbf{ip}+1\right)/2\right]$ – doubleOutput

On exit: the upper triangular part of the variance-covariance matrix of the ip parameter estimates given in b. They are stored packed by column, i.e., the covariance between the parameter estimate given in $\mathbf{b}\left[\mathit{i}\right]$ and the parameter estimate given in $\mathbf{b}\left[\mathit{j}\right]$, $\mathit{j}\ge \mathit{i}$, is stored in $\mathbf{cov}\left[\mathit{j}\left(\mathit{j}+1\right)/2+\mathit{i}\right]$, for $\mathit{i}=0,1,\dots ,\mathbf{ip}-1$ and $\mathit{j}=\mathit{i},\dots ,\mathbf{ip}-1$.

11:  $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_2_INT_ARG_GE

On entry, $\mathbf{nclin}=〈\mathit{\text{value}}〉$ while $\mathbf{ip}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{nclin}<\mathbf{ip}$.

NE_2_INT_ARG_LT

On entry, $\mathbf{tdc}=〈\mathit{\text{value}}〉$ while $\mathbf{nclin}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{tdc}\ge \mathbf{nclin}$.

On entry, $\mathbf{tdv}=〈\mathit{\text{value}}〉$ while $\mathbf{ip}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{tdv}\ge \mathbf{ip}+6$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_INT_ARG_LE

On entry, $\mathbf{nclin}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nclin}>0$.

NE_INT_ARG_LT

On entry, $\mathbf{ip}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ip}\ge 1$.

NE_MAT_NOT_FULL_RANK

Matrix c does not give a model of full rank.

NE_REAL_ARG_LE

On entry, scale must not be less than or equal to 0.0: $\mathbf{scale}=〈\mathit{\text{value}}〉$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g02gkce.c)

10.2

Program Data

Program Data (g02gkce.d)

10.3

Program Results

Program Results (g02gkce.r)