NAG Library Routine Document
G02BHF
1 Purpose
G02BHF computes means and standard deviations, sums of squares and cross-products of deviations from means, and Pearson product-moment correlation coefficients for selected variables omitting completely any cases with a missing observation for any variable (either over all variables in the dataset or over only those variables in the selected subset).
2 Specification
SUBROUTINE G02BHF ( |
N, M, X, LDX, MISS, XMISS, MISTYP, NVARS, KVAR, XBAR, STD, SSP, LDSSP, R, LDR, NCASES, IFAIL) |
INTEGER |
N, M, LDX, MISS(M), MISTYP, NVARS, KVAR(NVARS), LDSSP, LDR, NCASES, IFAIL |
REAL (KIND=nag_wp) |
X(LDX,M), XMISS(M), XBAR(NVARS), STD(NVARS), SSP(LDSSP,NVARS), R(LDR,NVARS) |
|
3 Description
The input data consists of
n observations for each of
m variables, given as an array
where
xij is the
ith observation on the
jth variable, together with the subset of these variables,
v1,v2,…,vp, for which information is required.
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 jth variable is denoted by xmj. Missing values need not be specified for all variables. The missing values can be utilized in two slightly different ways; you can indicate which scheme is required.
Firstly, let
wi=0 if observation
i contains a missing value for any of those variables in the set
1,2,…,m for which missing values have been declared, i.e., if
xij=xmj for any
j (
j=1,2,…,m) for which an
xmj has been assigned (see also
Section 7); and
wi=1 otherwise, for
i=1,2,…,n.
Secondly, let
wi=0 if observation
i contains a missing value for any of those variables in the selected subset
v1,v2,…,vp for which missing values have been declared, i.e., if
xij=xmj for any
j (
j=v1,v2,…,vp) for which an
xmj has been assigned (see also
Section 7); and
wi=1 otherwise, for
i=1,2,…,n.
The quantities calculated are:
(a) |
Means:
|
(b) |
Standard deviations:
|
(c) |
Sums of squares and cross-products of deviations from means:
|
(d) |
Pearson product-moment correlation coefficients:
If Sjj or Skk is zero, Rjk is set to zero. |
4 References
None.
5 Parameters
- 1: N – INTEGERInput
On entry: n, the number of observations or cases.
Constraint:
N≥2.
- 2: M – INTEGERInput
On entry: m, the number of variables.
Constraint:
M≥2.
- 3: X(LDX,M) – REAL (KIND=nag_wp) arrayInput
On entry: Xij must be set to xij, the value of the ith observation on the jth variable, for i=1,2,…,n and j=1,2,…,m.
- 4: LDX – INTEGERInput
On entry: the first dimension of the array
X as declared in the (sub)program from which G02BHF is called.
Constraint:
LDX≥N.
- 5: MISS(M) – INTEGER arrayInput/Output
On entry:
MISSj must be set equal to
1 if a missing value,
xmj, is to be specified for the
jth 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.
On exit: the array
MISS is overwritten by the routine, and the information it contained on entry is lost.
- 6: XMISS(M) – REAL (KIND=nag_wp) arrayInput/Output
On entry:
XMISSj must be set to the missing value,
xmj, to be associated with the
jth variable in the array
X, for those variables for which missing values are specified by means of the array
MISS (see
Section 7).
On exit: the array
XMISS is overwritten by the routine, and the information it contained on entry is lost.
- 7: MISTYP – INTEGERInput
On entry: indicates the manner in which missing observations are to be treated.
- MISTYP=1
- A case is excluded if it contains a missing value for any of the variables 1,2,…,m.
- MISTYP=0
- A case is excluded if it contains a missing value for any of the p≤m variables specified in the array KVAR.
- 8: NVARS – INTEGERInput
On entry: p, the number of variables for which information is required.
Constraint:
2≤NVARS≤M.
- 9: KVAR(NVARS) – INTEGER arrayInput
On entry:
KVARj must be set to the column number in
X of the
jth variable for which information is required, for
j=1,2,…,p.
Constraint:
1≤KVARj≤M, for j=1,2,…,p.
- 10: XBAR(NVARS) – REAL (KIND=nag_wp) arrayOutput
On exit: the mean value, of
x-j, of the variable specified in KVARj, for j=1,2,…,p.
- 11: STD(NVARS) – REAL (KIND=nag_wp) arrayOutput
On exit: the standard deviation,
sj, of the variable specified in KVARj, for j=1,2,…,p.
- 12: SSP(LDSSP,NVARS) – REAL (KIND=nag_wp) arrayOutput
On exit: SSPjk is the cross-product of deviations, Sjk, for the variables specified in KVARj and KVARk, for j=1,2,…,p and k=1,2,…,p.
- 13: LDSSP – INTEGERInput
On entry: the first dimension of the array
SSP as declared in the (sub)program from which G02BHF is called.
Constraint:
LDSSP≥NVARS.
- 14: R(LDR,NVARS) – REAL (KIND=nag_wp) arrayOutput
On exit: Rjk is the product-moment correlation coefficient, Rjk, between the variables specified in KVARj and KVARk, for j=1,2,…,p and k=1,2,…,p.
- 15: LDR – INTEGERInput
On entry: the first dimension of the array
R as declared in the (sub)program from which G02BHF is called.
Constraint:
LDR≥NVARS.
- 16: NCASES – INTEGEROutput
On exit: the number of cases actually used in the calculations (when cases involving missing values have been eliminated).
- 17: IFAIL – INTEGERInput/Output
-
On entry:
IFAIL must be set to
0,
-1 or 1. If you are unfamiliar with this parameter you should refer to
Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
-1 or 1 is recommended. If the output of error messages is undesirable, then the value
1 is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
0.
When the value -1 or 1 is used it is essential to test the value of IFAIL on exit.
On exit:
IFAIL=0 unless the routine detects an error or a warning has been flagged (see
Section 6).
6 Error Indicators and Warnings
If on entry
IFAIL=0 or
-1, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
Errors or warnings detected by the routine:
- IFAIL=1
-
- IFAIL=2
-
On entry, | NVARS<2, |
or | NVARS>M. |
- IFAIL=3
-
On entry, | LDX<N, |
or | LDSSP<NVARS, |
or | LDR<NVARS. |
- IFAIL=4
-
On entry, | KVARj<1, |
or | KVARj>M for some j=1,2,…,NVARS. |
- IFAIL=5
- IFAIL=6
-
After observations with missing values were omitted, no cases remained.
- IFAIL=7
-
After observations with missing values were omitted, only one case remained.
7 Accuracy
G02BHF does not use additional precision arithmetic for the accumulation of scalar products, so there may be a loss of significant figures for large n.
You are warned of the need to exercise extreme care in your selection of missing values. G02BHF treats all values in the inclusive range
1±0.1X02BEF-2×xmj, where
xmj is the missing value for variable
j specified in
XMISS.
You must therefore ensure that the missing value chosen for each variable is sufficiently different from all valid values for that variable so that none of the valid values fall within the range indicated above.
8 Further Comments
The time taken by G02BHF depends on n and p, and the occurrence of missing values.
The routine uses a two-pass algorithm.
9 Example
This example reads in a set of data consisting of five observations on each of four variables. Missing values of 0.0 are declared for the second and fourth variables; no missing values are specified for the first and third variables. The means, standard deviations, sums of squares and cross-products of deviations from means, and Pearson product-moment correlation coefficients for the fourth, first and second variables are then calculated and printed, omitting completely all cases containing missing values for these three selected variables; cases 3 and 4 are therefore eliminated, leaving only three cases in the calculations.
9.1 Program Text
Program Text (g02bhfe.f90)
9.2 Program Data
Program Data (g02bhfe.d)
9.3 Program Results
Program Results (g02bhfe.r)