naginterfaces.library.correg.mixeff_​hier_​init

naginterfaces.library.correg.mixeff_hier_init(dat, levels, y, fixed, rndm, wt=None)

mixeff_hier_init preprocesses a dataset prior to fitting a linear mixed effects regression model of the following form via either mixeff_hier_reml() or mixeff_hier_ml().

Deprecated since version 27.0.0.0: mixeff_hier_init is deprecated. Please use lmm_init() instead. See also the Replacement Calls document.

For full information please refer to the NAG Library document for g02jc

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g02/g02jcf.html

Parameters

datfloat, array-like, shape $(n,\text{ncol})$

A matrix of data, with $dat[i-1,j-1]$ holding the $i$th observation on the $j$th variable. The two design matrices $X$ and $Z$ are constructed from $dat$ and the information given in $fixed$ (for $X$) and $rndm$ (for $Z$).

levelsint, array-like, shape $\left(\text{ncol}\right)$

$levels[i-1]$ contains the number of levels associated with the $i$th variable held in $dat$.

If the $i$th variable is continuous or binary (i.e., only takes the values zero or one), then $levels[i-1]$ must be set to $1$.

Otherwise the $i$th variable is assumed to take an integer value between $1$ and $levels[i-1]$, (i.e., the $i$th variable is discrete with $levels[i-1]$ levels).

yfloat, array-like, shape $\left(n\right)$

$y$, the vector of observations on the dependent variable.

fixedint, array-like, shape $\left(\text{lfixed}\right)$

Defines the structure of the fixed effects design matrix, $X$.

$fixed\left[0\right]$

The number of variables, $N_F$, to include as fixed effects (not including the intercept if present).

$fixed\left[1\right]$

The fixed intercept flag which must contain $1$ if a fixed intercept is to be included and $0$ otherwise.

$fixed[2+i-1]$

The column of $dat$ holding the $\text{i}$th fixed variable, for $\text{i}=1,2,\dots ,fixed\left[0\right]$.

See Construction of the fixed effects design matrix, X for more details on the construction of $X$.

rndmint, array-like, shape $(:,\text{nrndm})$

$rndm[i-1,j-1]$ defines the structure of the random effects design matrix, $Z$. The $b$th column of $rndm$ defines a block of columns in the design matrix $Z$.

$rndm[0,b-1]$

The number of variables, $N_{R_b}$, to include as random effects in the $b$th block (not including the random intercept if present).

$rndm[1,b-1]$

The random intercept flag which must contain $1$ if block $b$ includes a random intercept and $0$ otherwise.

$rndm[2+i-1,b-1]$

The column of $dat$ holding the $\text{i}$th random variable in the $b$th block, for $\text{i}=1,2,\dots ,rndm[0,b-1]$.

$rndm[3+N_{R_b}-1,b-1]$

The number of subject variables, $N_{S_b}$, for the $b$th block. The subject variables define the nesting structure for this block.

$rndm[3+N_{R_b}+i-1,b-1]$

The column of $dat$ holding the $\text{i}$th subject variable in the $b$th block, for $\text{i}=1,2,\dots ,rndm[3+N_{R_b}-1,b-1]$.

See Construction of random effects design matrix, Z for more details on the construction of $Z$.

wtNone or float, array-like, shape $(:)$, optional

Note: the required length for this argument is determined as follows: if $wt\text{is not}None$: $n$; otherwise: $0$.

Optionally, the weights to be used in the weighted regression.

If $wt[i-1]=0.0$, the $i$th observation is not included in the model, in which case the effective number of observations is the number of observations with nonzero weights.

If weights are not provided then $wt$ must be set to None and the effective number of observations is $\text{n}$.

Returns

nffint

$p$, the number of fixed effects estimated, i.e., the number of columns in the design matrix $X$.

nlsvint

The number of levels for the overall subject variable (see Construction of random effects design matrix, Z for a description of what this means). If there is no overall subject variable, $nlsv=1$.

nrfint

The number of random effects estimated in each of the overall subject blocks. The number of columns in the design matrix $Z$ is given by $q=nrf\times nlsv$.

commdict, communication object

Communication structure.

Raises

NagValueError

(errno $2$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 1$.

(errno $3$)

On entry, $\text{ncol}=⟨value⟩$.

Constraint: $\text{ncol}\ge 0$.

(errno $4$)

On entry, variable $j$ of observation $i$ is less than $1$ or greater than $levels[j-1]$: $i=⟨value⟩$, $j=⟨value⟩$, value $=⟨value⟩$, $levels[j-1]=⟨value⟩$.

(errno $6$)

On entry, $levels[⟨value⟩]=⟨value⟩$.

Constraint: $levels[i-1]\ge 1$.

(errno $8$)

On entry, $wt[⟨value⟩]=⟨value⟩$.

Constraint: $wt[i-1]\ge 0.0$.

(errno $9$)

On entry, number of fixed parameters, $⟨value⟩$ is less than zero.

(errno $10$)

On entry, $\text{lfixed}=⟨value⟩$.

Constraint: $\text{lfixed}\ge ⟨value⟩$.

(errno $11$)

On entry, $\text{nrndm}=⟨value⟩$.

Constraint: $\text{nrndm}>0$.

(errno $12$)

On entry, number of random parameters for random statement $i$ is less than $0$: $i=⟨value⟩$, number of parameters $=⟨value⟩$.

(errno $102$)

On entry, more fixed factors than observations, $n=⟨value⟩$.

Constraint: $n\ge ⟨value⟩$.

(errno $108$)

On entry, no observations due to zero weights.

(errno $109$)

On entry, invalid value for fixed intercept flag: value $=⟨value⟩$.

(errno $112$)

On entry, invalid value for random intercept flag for random statement $i$: $i=⟨value⟩$, value $=⟨value⟩$.

(errno $209$)

On entry, index of fixed variable $j$ is less than $1$ or greater than $\text{ncol}$: $j=⟨value⟩$, index $=⟨value⟩$ and $\text{ncol}=⟨value⟩$.

(errno $212$)

On entry, must be at least one parameter, or an intercept in each random statement $i$: $i=⟨value⟩$.

(errno $312$)

On entry, index of random variable $j$ in random statement $i$ is less than $1$ or greater than $\text{ncol}$: $i=⟨value⟩$, $j=⟨value⟩$, index $=⟨value⟩$ and $\text{ncol}=⟨value⟩$.

(errno $412$)

On entry, number of subject parameters for random statement $i$ is less than $0$: $i=⟨value⟩$, number of parameters $=⟨value⟩$.

(errno $512$)

On entry, nesting variable $j$ in random statement $i$ has one level: $j=⟨value⟩$, $i=⟨value⟩$.

Notes

mixeff_hier_init must be called prior to fitting a linear mixed effects regression model with either mixeff_hier_reml() or mixeff_hier_ml().

The model fitting functions mixeff_hier_reml() and mixeff_hier_ml() fit a model of the following form:

$$y=X\beta +Z\nu +ϵ$$

where	$y$ is a vector of $n$ observations on the dependent variable,
	$X$ is an $n\times p$ design matrix of fixed independent variables,
	$\beta$ is a vector of $p$ unknown fixed effects,
	$Z$ is an $n\times q$ design matrix of random independent variables,
	$\nu$ is a vector of length $q$ of unknown random effects,
	$ϵ$ is a vector of length $n$ of unknown random errors,

and $\nu$ and $ϵ$ are Normally distributed with expectation zero and variance/covariance matrix defined by

$$\begin{array}{c}Var\left[\begin{array}{c}\nu \\ ϵ\end{array}\right]=\left[\begin{array}{cc}G& 0\\ 0& R\end{array}\right]\end{array}$$

where $R={\sigma }_R^{2}I$, $I$ is the $n\times n$ identity matrix and $G$ is a diagonal matrix.

Case weights can be incorporated into the model by replacing $X$ and $Z$ with $W_c^{1/2}X$ and $W_c^{1/2}Z$ respectively where $W_c$ is a diagonal weight matrix.