naginterfaces.library.correg.coeffs_​pearson_​miss_​case

naginterfaces.library.correg.coeffs_pearson_miss_case(x, miss, xmiss)

coeffs_pearson_miss_case computes means and standard deviations of variables, sums of squares and cross-products of deviations from means, and Pearson product-moment correlation coefficients for a set of data omitting completely any cases with a missing observation for any variable.

For full information please refer to the NAG Library document for g02bb

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/g02/g02bbf.html

Parameters

xfloat, array-like, shape $(n,m)$

$x[\text{i}-1,\text{j}-1]$ must be set to $x_{\text{i}\text{j}}$, the value of the $\text{i}$th observation on the $\text{j}$th variable, for $\text{j}=1,2,\dots ,m$, for $\text{i}=1,2,\dots ,n$.

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

$miss[j-1]$ must be set equal to $1$ if a missing value, $x{m}_j$, is to be specified for the $j$th variable in the array $x$, or set equal to $0$ otherwise. Values of $miss$ must be given for all $m$ variables in the array $x$.

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

$xmiss[j-1]$ must be set to the missing value, $x{m}_j$, to be associated with the $j$th variable in the array $x$, for those variables for which missing values are specified by means of the array $miss$ (see Accuracy).

Returns

xbarfloat, ndarray, shape $\left(m\right)$

The mean value, ${\overline{x}}_{\text{j}}$, of the $\text{j}$th variable, for $\text{j}=1,2,\dots ,m$.

stdfloat, ndarray, shape $\left(m\right)$

The standard deviation, $s_{\text{j}}$, of the $\text{j}$th variable, for $\text{j}=1,2,\dots ,m$.

sspfloat, ndarray, shape $(m,m)$

$ssp[\text{j}-1,\text{k}-1]$ is the cross-product of deviations $S_{\text{j}\text{k}}$, for $\text{k}=1,2,\dots ,m$, for $\text{j}=1,2,\dots ,m$.

rfloat, ndarray, shape $(m,m)$

$r[\text{j}-1,\text{k}-1]$ is the product-moment correlation coefficient $R_{\text{j}\text{k}}$ between the $\text{j}$th and $\text{k}$th variables, for $\text{k}=1,2,\dots ,m$, for $\text{j}=1,2,\dots ,m$.

ncasesint

The number of cases actually used in the calculations (when cases involving missing values have been eliminated).

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 2$.

(errno $2$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge 2$.

(errno $4$)

After observations with missing values were omitted, no cases remained.

(errno $5$)

After observations with missing values were omitted, only one case remained.

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

The input data consist of $n$ observations for each of $m$ variables, given as an array

$$\left[x_{ij}\right]\text{,}i=1,2,\dots ,n(n\ge 2),j=1,2,\dots ,m(m\ge 2)\text{,}$$

where $x_{ij}$ is the $i$th observation on the $j$th variable. In addition, each of the $m$ variables may optionally have associated with it a value which is to be considered as representing a missing observation for that variable; the missing value for the $j$th variable is denoted by $x{m}_j$. Missing values need not be specified for all variables.

Let $w_i=0$ if observation $i$ contains a missing value for any of those variables for which missing values have been declared, i.e., if $x_{ij}=x{m}_j$ for any $j$ for which an $x{m}_j$ has been assigned (see also Accuracy); and $w_i=1$ otherwise, for $\text{i}=1,2,\dots ,n$.

The quantities calculated are:

1. Means:

   $${\overline{x}}_j=\frac{{\sum }_{i=1}^n{w}_i{x}_{ij}}{{\sum }_{i=1}^n{w}_i}\text{,}j=1,2,\dots ,m\text{.}$$

2. Standard deviations:

   $$s_j=\sqrt{\frac{{\sum }_{i=1}^n{w}_i{(x_{ij}-{\overline{x}}_j)}^2}{{\sum }_{i=1}^n{w}_i-1}}\text{,}j=1,2,\dots ,m\text{.}$$

3. Sums of squares and cross-products of deviations from means:

   $$S_{jk}=\sum _{i=1}^n{w}_i(x_{ij}-{\overline{x}}_j)(x_{ik}-{\overline{x}}_k)\text{,}j,k=1,2,\dots ,m\text{.}$$

4. Pearson product-moment correlation coefficients:

   $$R_{jk}=\frac{S_{jk}}{\sqrt{S_{jj}{S}_{kk}}}\text{,}j,k=1,2,\dots ,m\text{.}$$

   If $S_{jj}$ or $S_{kk}$ is zero, $R_{jk}$ is set to zero.