# Proc Discrim and interpretation

#### masarimk

##### Member
Dear All,

I have to analyze a small data set. 6 variables and 20 observation. I clustered 20 observation into 3 groups and I used Proc Discrim and SAS output 3 functions. Below is the output;
Linear Discriminant Function for CLUSTER

PHP:
            Variable        Label             1                 2                    3

Constant                     -135.43350    -240.07241     -108.59505
x1              x1          11.40796        6.74077           6.25519
x2              x2          18.17754        27.15047         14.51286
x3              x3          8.27477         6.69168           1.46474
x4              x4         12.85626        24.54617         14.64702
x5              x5          8.03166         12.66484         13.85583
x6              x6          8.90164         14.04415         9.92077
It outputs 3 functions because I have 3 clusters? How do I interpret these coefficients?
Thank you.

#### Janus

##### New Member
For each class you can derive a class score based on the linear coefficients (imagine it as you would OLS). If you are only interested in classifying observations based on their maximum class score, you can stop here. If you want to get at class probabilities, then please see page 2 of this pdf: http://sites.stat.psu.edu/~jiali/course/stat597e/notes2/lda.pdf

Note, I have seen empirical priors used to estimate pi, and I have also seen naive methods that assign an equal value to pi for each class (e.g., with three classes, pi for each class = 1/3).

#### fisch

##### New Member
Hi Janus,

could you explain how I transform the SAS-Output into probabilities? I dont think, that the function f(x) from the file is the Funktion for each class from above. Do I have to derive it or something?

Thanks, fisch