naginterfaces.library.correg.linregm_​obs_​edit

naginterfaces.library.correg.linregm_obs_edit(update, isx, q, x, ix, y, rss, mean='M', wt=None)

linregm_obs_edit adds or deletes an observation from a general regression model fitted by linregm_fit().

For full information please refer to the NAG Library document for g02dc

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g02/g02dcf.html

Parameters

updatestr, length 1

Indicates if an observation is to be added or deleted.

$update=\text{'A'}$

The observation is added.

$update=\text{'D'}$

The observation is deleted.

isxint, array-like, shape $\left(m\right)$

If $isx[\text{j}-1]$ is greater than $0$, the value contained in $x[(\text{j}-1)\times ix]$ is to be included as a value of $x^T$, for $\text{j}=1,2,\dots ,m$.

qfloat, array-like, shape $(\text{ip},\text{ip}+1)$

Must be array $q$ as output by linregm_fit(), linregm_var_add(), linregm_var_del() or linregm_fit_onestep(), or a previous call to linregm_obs_edit.

xfloat, array-like, shape $((m-1)\times ix+1)$

The $\text{ip}$ values for the dependent variables of the new observation, $x^T$. The positions will depend on the value of $ix$.

ixint

The increment for elements of $x$. Two situations are common:

$ix=1$

The values of $x$ are to be chosen from consecutive locations in $x$, i.e., $x\left[0\right],x\left[1\right],\dots ,x[m-1]$.

$ix=\text{ldx}$

The values of $x$ are to be chosen from a row of a two-dimensional array with first dimension $\text{ldx}$, i.e., $x\left[0\right],x\left[\text{ldx}\right],\dots ,x\left[(m-1)\text{ldx}\right]$.

yfloat

The value of the dependent variable for the new observation, $y_{\text{new}}$.

rssfloat

The value of the residual sums of squares for the original set of observations.

meanstr, length 1, optional

Indicates if a mean has been used in the model.

$mean=\text{'M'}$

A mean term or intercept will have been included in the model by linregm_fit().

$mean=\text{'Z'}$

A model with no mean term or intercept will have been fitted by linregm_fit().

wtNone or float, optional

If provided, $wt$ must contain the weight to be used with the new observation.

If $wt$ is None, the observation is not included in the model.

Returns

qfloat, ndarray, shape $(\text{ip},\text{ip}+1)$

The first $\text{ip}$ elements of the first column of $q$ will contain $c_1^{\ast }$ the upper triangular part of columns $2$ to $\text{ip}+1$ will contain $R^{\ast }$ the remainder is unchanged.

rssfloat

The updated values of the residual sums of squares.

Note: this will only be valid if the model is of full rank.

Raises

NagValueError

(errno $1$)

On entry, $⟨value⟩$ elements of $isx>0$ instead of $\text{ip}-1$ (for mean) $=⟨value⟩$.

(errno $1$)

On entry, $ix=⟨value⟩$.

Constraint: $ix\ge 1$.

(errno $1$)

On entry, $⟨value⟩$ elements of $isx>0$ instead of $\text{ip}=⟨value⟩$.

(errno $1$)

On entry, $mean=⟨value⟩$.

Constraint: $mean=\text{'M'}$ or $\text{'Z'}$.

(errno $1$)

On entry, $rss=⟨value⟩$.

Constraint: $rss\ge 0.0$.

(errno $1$)

On entry, $update=⟨value⟩$.

Constraint: $update=\text{'A'}$ or $\text{'D'}$.

(errno $1$)

On entry, $\text{weight}=⟨value⟩$.

Constraint: $\text{weight}=\text{'U'}$ or $\text{'W'}$.

(errno $1$)

On entry, $\text{ip}=⟨value⟩$.

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

(errno $2$)

On entry, $wt=⟨value⟩$.

Constraint: $wt\ge 0.0$.

(errno $3$)

The $R$ matrix could not be updated.

(errno $4$)

The residual sums of squares cannot be updated.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

linregm_fit() fits a general linear regression model to a dataset. You may wish to change the model by either adding or deleting an observation from the dataset. linregm_obs_edit takes the results from linregm_fit() and makes the required changes to the vector $c$ and the upper triangular matrix $R$ produced by linregm_fit(). The regression coefficients, standard errors and the variance-covariance matrix of the regression coefficients can be obtained from linregm_update() after all required changes to the dataset have been made.

linregm_fit() performs a $QR$ decomposition on the (weighted) $X$ matrix of independent variables. To add a new observation to a model with $p$ parameters, the upper triangular matrix $R$ and vector $c_1$ (the first $p$ elements of $c$) are augmented by the new observation on independent variables in $x^T$ and dependent variable $y_{\text{new}}$. Givens rotations are then used to restore the upper triangular form.

$$\begin{array}{c}\left(\begin{array}{c}R:c_1\\ x:y_{\text{new}}\end{array}\right)\to \left(\begin{array}{c}{R}^{\ast }:c_1^{\ast }\\ 0:y_{\text{new}}^{\ast }\end{array}\right)\text{.}\end{array}$$

Note: only $R$ and the upper part of $c$ are updated the remainder of the $Q$ matrix is unchanged.

References

Golub, G H and Van Loan, C F, 1996, Matrix Computations, (3rd Edition), Johns Hopkins University Press, Baltimore

Hammarling, S, 1985, The singular value decomposition in multivariate statistics, SIGNUM Newsl. (20(3)), 2–25