Discriminant How To
Transcript of Discriminant How To
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Discriminant Function Analysis in SPSS
To do DFA in SPSS, start from “Classify” in the “Analyze” menu (because we’re trying toclassify participants into different groups). In this case we’re looking at a dataset that describes
children with ADHD. Research tells us that the degree of symptom impairment in childhood
disorders is often in the eye of the beholder—some adults may think that a child has difficulty
behaving, and other adults may not see it as a problem. For instance mothers (who are still mostoften the child’s primary caregiver) may think that a child has difficulty sitting still, while fathers
(who may see the child primarily in less-structured “play” settings) may believe the behavior is
“just kids being kids.” We’re going to look at whether the symptoms reported on four differentmeasures (q1, q2, q3, and q4) can tell us whether those symptom ratings were provided by the
child’s mother (“parent” = 1) or by the child’s father (“parent” = 2).
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In the dialog box, put in “parent” as the “grouping variable” (in other words, the variable that
you think defines different groups—your criterion variable for the analysis). It will appear in the box with two question marks after it—you have to tell SPSS what the codes are for the two
groups that you want to compare. Hit “Define Range” and type in “1” and “2” as the different
values of the “parent” variable that you want to compare. Then hit “Continue” to go on.
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Now put the four “question” variables (q1-q4) in as the predictors (“independents”):
Hit the “Statistics” button to go on.
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This sub-dialog box lets you see descriptive statistics on each predictor variable for the different
groups. Let’s check “Means” to see some basic descriptive stats.
Hit “Continue” to go back to the main dialog box.
Then, in the main dialog box, hit the “Classify” button to see the next sub-dialog.
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Here’s the sub-dialog that you get when you hit the “Classify” button:
On this screen, check the box for the “summary table.” This will give you the classification table(sensitivity, specificity, etc.) on your printout.
Hit “Continue” to go back to the main dialog box, and then hit “OK” to see the results of your
analysis.
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Here are the results:
Anal ysis Case Processi ng Summary
Unweighted Cases N Percent
Valid 89 97.8
Excluded Missing or out-of-range group codes 0 .0
At least one missing discriminating
variable
2 2.2
Both missing or out-of-range group
codes and at least one missing
discriminating variable
0 .0
Total 2 2.2
Total 91 100.0
This table just tells you if there’s any missing data.
Group Statistics
Mother or Father?
Mean Std. Deviation
Valid N (listwise)
Unweighted Weighted
Father Question 1 1.54 .519 13 13.000
Question 2 1.00 .000 13 13.000
Question 3 1.92 1.038 13 13.000
Question 4 1.62 .870 13 13.000
Mother Question 1 2.41 .819 76 76.000
Question 2 2.67 .598 76 76.000
Question 3 2.17 .915 76 76.000
Question 4 1.82 .905 76 76.000
Total Question 1 2.28 .839 89 89.000
Question 2 2.43 .810 89 89.000
Question 3 2.13 .932 89 89.000
Question 4 1.79 .898 89 89.000
This table shows the means that we asked for—it gives means on each variable for people in
each sub-group, and also the overall means on each variable.
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Summary of Canonical Discriminant Functions
Eigenvalues
Function
Eigenvalue % of Variance Cumulative %
Canonical
Correlation
dimension0
1 1.387a 100.0 100.0 .762
a. First 1 canonical discriminant functions were used in the analysis.
This table tells you something about the “latent variable” that you’ve constructed (i.e., thediscriminant function), which helps you to differentiate between the groups. For more about
eigenvalues, see the website information on the topic of Factor Analysis.
Wilks' Lambda
Test of Function(s) Wilks' Lambda Chi-square df Sig.
dimension0
1 .419 73.945 4 .000
Here’s the multivariate test—Wilks’ lambda, just like in MANOVA. Because p < .05, we cansay that the model is a good fit for the data. This multivariate test is a goodness of fit statistic,
just like the F -test is for regression.
Standardized Canonical
Discriminant Function
Coefficients
Function
1
Question 1 .149
Question 2 1.007
Question 3 .049
Question 4 .382
These “discriminant function coefficients” work just like the beta-weights in regression. Based
on these, we can write out the equation for the discriminant function:
DF = .149*q1 + 1.007*q2 + .049*q3 + .382*q4
Using this equation, given someone’s scores on q1, q2, q3, and q4, we can calculate their score
on the discriminant function. To figure out what that DF score means, look at the group
centroids, below.
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Structure Matrix
Function
1
Question 2 .914
Question 1 .336
Question 3 .081
Question 4 .068
Pooled within-groups correlations
between discriminating variables
and standardized canonical
discriminant functions
Variables ordered by absolute
size of correlation within function.
Ignore this table—it tells you the correlation between each item and the discriminant function,
but we won’t use it for anything here. Make sure that you aren’t looking at the “structurematrix” when you get the coefficients for the discriminant function. Those come from the table
called “standardized canonical discriminant function coefficients” (which looks a lot like this
one, but isn’t the same).
Functions at Group Centroids
Mother or Father? Function
1
dimension0
Father -2.815
Mother .482
Unstandardized canonical discriminant
functions evaluated at group means
Here are the group centroids. If someone’s score on the discriminant function is closer to –2.815, then those answers were probably the child’s father. If the person’s score on the DF is
closer to .482, then the data probably came from the child’s mother. In practical terms, we
usually figure out which group a person is in by calculating a cut score halfway between the two
centroids:
Cut Score = (-2.815 + .482) / 2 = -1.167
If an individual person’s score on the DF (calculated by plugging in their scores on q1, q2, q3,
and q4 to the DF equation we wrote out above) is above –1.167, then they were probably the
child’s mother. If their DF score is below –1.167, then they were probably the child’s father.
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Classification Statistics
Classification Processing Summary
Processed 91
Excluded Missing or out-of-range group codes 0
At least one missing discriminating
variable
2
Used in Output 89
Prior Probabilities for Groups
Mother or Father?
Prior
Cases Used in Analysis
Unweighted Weighted
dimension0
Father .500 13 13.000
Mother .500 76 76.000
Total 1.000 89 89.000
Classification Resultsa
Mother or Father? Predicted Group Membership
TotalFather Mother
Original Count
dimension2
Father 13 0 13
Mother 6 70 76
%
dimension2
Father 100.0 .0 100.0
Mother 7.9 92.1 100.0
a. 93.3% of original grouped cases correctly classified.
Here’s the classification table that we got by selecting that option in the SPSS dialog box. Like
the table shown in this week’s class notes, it gives information about actual group membershipvs. predicted group membership.
--Overall % correctly classified = 93.3%--Sensitivity = 13 / 13 = 100%
--Specificity = 70 / 76 = 92.1%
Looking at the columns in this table instead of the rows, you can also calculate PPV and NPV:--PPV = 13 / (13+6) = 68.4%
--NPV = 70 / 70 = 100%
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Now let’s go back to the main dialog box for DFA, and try a stepwise procedure instead.
The only change needed is to change this radio button to “use stepwise method.” Now SPSS willselect the best predictor or set of predictors from the four original possibilities.
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If you click on the “Method” button (which was grayed-out before, but becomes active once you
select “Use Stepwise Method”), you will see the following dialog box. Take a look at it—it tellsSPSS how to do the steps, and when to stop adding steps. Just leave everything here on its
default settings—no need to make any changes.
Hit “Continue” here, and then “OK” in the main dialog box to see your results.
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One last step—let’s get a graph of the different groups, based on the two best predictors (q2 and
q4). This gives us a visual representation that shows how the two groups separate out from oneanother using these two predictors.
Graphs are found in the “Graphs” menu in SPSS. We’ll use a scatterplot to show the
differentiation between the two groups. Newer versions of SPSS (v16.0 and higher) have aninteractive “chart builder” format for graphs, but I find it easier to create graphs using the
individual dialog boxes for specific types of graphs. These are similar to the way SPSS produced
graphs in versions 15.0 and lower, and can be found under the “Legacy Dialogs” submenu.
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This box appears. Leave the graph set on “Simple,” and hit the “Define” key to go on.
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Here’s the dialog box where you enter variables for the graph. Put q2 and q4 on the two axes of
the graph ( y and x-axes: it doesn’t really matter which one goes on which axis, but if you setthem up this way, your graph will look the same as mine. If you reverse them, it will look like
my graph turned on its side. Either way is correct).
The “Set Markers By…” command lets you show the two different groups on the DV (mothers
vs. fathers) in two different colors on the graph. This is how you will be able to see thedifferentiation between the two groups.
Hit “OK” to see the output.
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Here’s the graph:
You can see on this graph how the two groups are visually separated from one another, based on people’s answers to q2 and q4. Not all discriminant functions will separate groups this perfectly.
Sometimes you can find predictors that statistically differentiate between the groups, while the
graphical representation still shows the groups as pretty jumbled together.
Paul F. Cook, University of Colorado Denver, Center for Nursing ResearchRevised 1/10 with SPSS (PASW) version 18.0
Members of Group 1
Members of Group 2