⇤ ← Revision 1 as of 2009-01-30 09:48:08
310
Comment:
|
1637
|
Deletions are marked like this. | Additions are marked like this. |
Line 1: | Line 1: |
= Which output criteria should I use when using the casewise statistics option with the Normal discriminant method in SPSS? = | |
Line 2: | Line 3: |
= Which output criteria should I use when using the case statistics option with the Normal discriminant method in SPSS? = | The discriminant procedure, which is optimal when the groups follow a Normal distribution, uses the Mahalanobis distance (d) as a summary measure of the difference both between the groups and within each group. The Mahalanobis distance can also be [:FAQ/mahal used] as a means of identifying multivariate outliers. |
Line 4: | Line 5: |
The discriminant procedure, which is optimal when the groups follow a Normal distribution, uses the Mahalanobis distance as a summary measure of the difference between the groups. | There are two conditional probabilities outputted in tables using the ''casewise statistics'' option in SPSS. These are P(G=g conditional on D=d) and P(D>d conditional on G=g) for the predicted group with the former also outputted for the other groups. Here ''g ''represents the group of interest and ''d'' represents the outputted Mahalanobis distance for a particular case. In particular P(G=g conditional on D=d) is the posterior probability of a case falling in the predicted group (for which this probability is a maximum) based on that case's Mahalanobis distance. The Mahalanobis distance for a particular case represents how ''typical'' that case is with respect to other cases in the group, g. In particular it measures the standardised distance of a case from the centre of the group. For a particular group, g, the P(G=g conditional on D=d) equals in SPSS $$ \frac{\mbox{exp}(-0.5 d(g)^text{2})}{\sum_text{groups} \mbox{exp}(-0.5 d(group)^text{2})} $$ Since the Mahalanobis distance based on p predictors follows a chi-square distribution on p degrees of freedom if it is equal to zero. It follows P (D>d conditional on G=g) = 1 - $$\chi(p)$$ |
- = Which output criteria should I use when using the casewise statistics option with the Normal discriminant method in SPSS? =
The discriminant procedure, which is optimal when the groups follow a Normal distribution, uses the Mahalanobis distance (d) as a summary measure of the difference both between the groups and within each group. The Mahalanobis distance can also be [:FAQ/mahal used] as a means of identifying multivariate outliers.
There are two conditional probabilities outputted in tables using the casewise statistics option in SPSS. These are P(G=g conditional on D=d) and P(D>d conditional on G=g) for the predicted group with the former also outputted for the other groups. Here g represents the group of interest and d represents the outputted Mahalanobis distance for a particular case.
In particular P(G=g conditional on D=d) is the posterior probability of a case falling in the predicted group (for which this probability is a maximum) based on that case's Mahalanobis distance. The Mahalanobis distance for a particular case represents how typical that case is with respect to other cases in the group, g. In particular it measures the standardised distance of a case from the centre of the group.
For a particular group, g, the P(G=g conditional on D=d) equals in SPSS
$$ \frac{\mbox{exp}(-0.5 d(g)text{2})}{\sum_text{groups} \mbox{exp}(-0.5 d(group)text{2})} $$
Since the Mahalanobis distance based on p predictors follows a chi-square distribution on p degrees of freedom if it is equal to zero.
It follows
P (D>d conditional on G=g) = 1 - $$\chi(p)$$