Description
This is a ppt consists of discrimminant analysis concepts.
Discrimminant Analysis
Similarities and Differences between ANOVA, Regression, and Discriminant Analysis
Table 1
ANOVA REGRESSION One DISCRIMINANT ANALYSIS One
Similarities Number of dependent variables Number of independent variables
Differences Nature of the dependent variables Nature of the independent variables
One
Multiple
Multiple
Multiple
Metric Categorical
Metric Metric
Categorical Metric
Discriminant Analysis
Discriminant analysis is a technique for analyzing data when the criterion or dependent variable is categorical and the predictor or independent variables are interval in nature. The objectives of discriminant analysis are as follows: ? Development of discriminant functions, or linear combinations of the predictor or independent variables, which will best discriminate between the categories of the criterion or dependent variable (groups). ? Examination of whether significant differences exist among the groups, in terms of the predictor variables. ? Determination of which predictor variables contribute to most of the intergroup differences. ? Classification of cases to one of the groups based on the values of the predictor variables. ? Evaluation of the accuracy of classification.
Discriminant Analysis
?
?
?
?
When the criterion variable has two categories, the technique is known as two-group discriminant analysis. When three or more categories are involved, the technique is referred to as multiple discriminant analysis. The main distinction is that, in the two-group case, it is possible to derive only one discriminant function. The first function has the highest ratio of between-groups to within-groups sum of squares. The second function, uncorrelated with the first, has the second highest ratio, and so on. However, not all the functions may be statistically significant.
Discriminant Analysis Model
The discriminant analysis model involves linear combinations of the following form:
D = b0 + b1X1 + b2X2 + b3X3 + . . . + bkXk
where
D b 's X 's
?
= = =
discriminant score discriminant coefficient or weight predictor or independent variable
?
The coefficients, or weights (b), are estimated so that the groups differ as much as possible on the values of the discriminant function. This occurs when the ratio of between-group sum of squares to within-group sum of squares for the discriminant scores is at a maximum.
Statistics Associated with Discriminant Analysis
?
?
?
Canonical correlation. Canonical correlation measures the extent of association between the discriminant scores and the groups. Centroid. The centroid is the mean values for the discriminant scores for a particular group. There are as many centroids as there are groups. The means for a group on all the functions are the group centroids. Classification matrix. the classification matrix contains the number of correctly classified and misclassified cases.
Statistics Associated with Discriminant Analysis
?
?
?
Discriminant function coefficients. The discriminant function coefficients (unstandardized) are the multipliers of variables, when the variables are in the original units of measurement. Discriminant scores. The unstandardized coefficients are multiplied by the values of the variables. These products are summed and added to the constant term to obtain the discriminant scores. Eigenvalue. For each discriminant function, the Eigenvalue is the ratio of between-group to withingroup sums of squares. Large Eigenvalues imply superior functions.
Statistics Associated with Discriminant Analysis
?
F values and their significance. These are
?
?
calculated from a one-way ANOVA, with the grouping variable serving as the categorical independent variable. Each predictor, in turn, serves as the metric dependent variable in the ANOVA. Group means and group standard deviations. These are computed for each predictor for each group. Pooled within-group correlation matrix. The pooled within-group correlation matrix is computed by averaging the separate covariance matrices for all the groups.
Statistics Associated with Discriminant Analysis
?
?
?
?
Standardized discriminant function coefficients. These are the discriminant function coefficients and are used as the multipliers when the variables have been standardized to a mean of 0 and a variance of 1. Structure correlations. Also referred to as discriminant loadings, the structure correlations represent the simple correlations between the predictors and the discriminant function. Total correlation matrix. If the cases are treated as if they were from a single sample and the correlations computed, a total correlation matrix is obtained. Wilks' . Sometimes also called the U statistic, Wilks' for each predictor is the ratio of the within-group sum of squares to ? ? the total sum of squares. Its value varies between 0 and 1. Large values of (near 1) indicate that group means do not seem to be different. Small values of (near 0) indicate that ? the group means seem to be different.?
Conducting Discriminant Analysis
Fig. 1
Formulate the Problem
Estimate the Discriminant Function Coefficients
Determine the Significance of the Discriminant Function
Interpret the Results
Assess Validity of Discriminant Analysis
Conducting Discriminant Analysis
Formulate the Problem
?
?
?
?
?
?
Identify the objectives, the criterion variable, and the independent variables. The criterion variable must consist of two or more mutually exclusive and collectively exhaustive categories. The predictor variables should be selected based on a theoretical model or previous research, or the experience of the researcher. One part of the sample, called the estimation or analysis sample, is used for estimation of the discriminant function. The other part, called the holdout or validation sample, is reserved for validating the discriminant function. Often the distribution of the number of cases in the analysis and validation samples follows the distribution in the total sample.
Information on Resort Visits: Analysis Sample
Table 2
Resort Visit Annual Family Income ($000) Attitude Toward Travel Importance Household Age of Attached Size Head of to Family Household Vacation Amount Spent on Family Vacation
No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
50.2 70.3 62.9 48.5 52.7 75.0 46.2 57.0 64.1 68.1 73.4 71.9 56.2 49.3 62.0
5 6 7 7 6 8 5 2 7 7 6 5 1 4 5
8 7 5 5 6 7 3 4 5 6 7 8 8 2 6
3 4 6 5 4 5 3 6 4 5 5 4 6 3 2
43 61 52 36 55 68 62 51 57 45 44 64 54 56 58
M (2) H (3) H (3) L (1) H (3) H (3) M (2) M (2) H (3) H (3) H (3) H (3) M (2) H (3) H (3)
Information on Resort Visits: Analysis Sample
Table 2 cont.
Resort Visit 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Annual Family Income ($000) 32.1 36.2 43.2 50.4 44.1 38.3 55.0 46.1 35.0 37.3 41.8 57.0 33.4 37.5 41.3 Attitude Toward Travel 5 4 2 5 6 6 1 3 6 2 5 8 6 3 3 Importance Household Age of Attached Size Head of to Family Household Vacation 4 3 5 2 6 6 2 5 4 7 1 3 8 2 3 3 2 2 4 3 2 2 3 5 4 3 2 2 3 2 58 55 57 37 42 45 57 51 64 54 56 36 50 48 42 Amount Spent on Family Vacation L L M M M L M L L L M M L L L (1) (1) (2) (2) (2) (1) (2) (1) (1) (1) (2) (2) (1) (1) (1)
No.
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Information on Resort Visits: Holdout Sample
Table 3
Resort Visit Annual Family Income ($000) Attitude Toward Travel Importance Household Age of Attached Size Head of to Family Household Vacation Amount Spent on Family Vacation
No.
1 2 3 4 5 6 7 8 9 10 11 12
1 1 1 1 1 1 2 2 2 2 2 2
50.8 63.6 54.0 45.0 68.0 62.1 35.0 49.6 39.4 37.0 54.5 38.2
4 7 6 5 6 5 4 5 6 2 7 2
7 4 7 4 6 6 3 3 5 6 3 2
3 7 4 3 6 3 4 5 3 5 3 3
45 55 58 60 46 56 54 39 44 51 37 49
M(2) H (3) M(2) M(2) H (3) H (3) L (1) L (1) H (3) L (1) M(2) L (1)
Conducting Discriminant Analysis
Estimate the Discriminant Function Coefficients
The direct method involves estimating the discriminant function so that all the predictors are included simultaneously. In stepwise discriminant analysis, the predictor variables are entered sequentially, based on their ability to discriminate among groups.
?
?
Results of Two-Group Discriminant Analysis
Table 4
GROUP MEANS VISIT 1 2 Total
INCOME
60.52000 41.91333 51.21667
TRAVEL VACATION
5.40000 4.33333 4.86667 5.80000 4.06667 4.9333
HSIZE
4.33333 2.80000 3.56667
AGE
53.73333 50.13333 51.93333
Group Standard Deviations 1 2 Total 9.83065 7.55115 12.79523 1.91982 1.95180 1.97804 1.82052 2.05171 2.09981 1.23443 .94112 1.33089 HSIZE 8.77062 8.27101 8.57395 AGE
Pooled Within-Groups Correlation Matrix INCOME TRAVEL VACATION INCOME TRAVEL VACATION HSIZE AGE 1.00000 0.19745 0.09148 0.08887 - 0.01431 1.00000 0.08434 -0.01681 -0.19709
1.00000 0.07046 0.01742
1.00000 -0.04301
1.00000
Wilks' (U-statistic) and univariate F ratio with 1 and 28 degrees of freedom Variable INCOME TRAVEL VACATION HSIZE AGE Wilks' 0.45310 0.92479 0.82377 0.65672 0.95441 F 33.800 2.277 5.990 14.640 1.338 Significance 0.0000 0.1425 0.0209 0.0007 0.2572
Contd.
Results of Two-Group Discriminant Analysis
Table 4 cont.
CANONICAL DISCRIMINANT FUNCTIONS Function Eigenvalue % of Variance Cum Canonical After Wilks' % Correlation Function ? : 0 0 .3589 100.00 0.8007 : Chi-square df Significance 26.130 5 0.0001
1*
1.7862
100.00
* marks the 1 canonical discriminant functions remaining in the analysis. Standard Canonical Discriminant Function Coefficients FUNC INCOME TRAVEL VACATION HSIZE AGE 1
0.74301 0.09611 0.23329 0.46911 0.20922
Structure Matrix: Pooled within-groups correlations between discriminating variables & canonical discriminant functions (variables ordered by size of correlation within function)
FUNC
INCOME HSIZE VACATION TRAVEL AGE
1
0.82202 0.54096 0.34607 0.21337 0.16354 Contd.
Results of Two-Group Discriminant Analysis
Table 4 cont.
Unstandardized Canonical Discriminant Function Coefficients INCOME TRAVEL VACATION HSIZE AGE (constant) FUNC 1 0.8476710E-01 0.4964455E-01 0.1202813 0.4273893 0.2454380E-01 -7.975476 Canonical discriminant functions evaluated at group means (group centroids) Group 1 2 FUNC 1 1.29118 -1.29118
Classification results for cases selected for use in analysis Actual Group Group Group 1 2 Predicted No. of Cases 15 15 Group Membership 1 2 12 80.0% 0 0.0% 3 20.0% 15 100.0% Contd.
Percent of grouped cases correctly classified: 90.00%
Results of Two-Group Discriminant Analysis
Table 4 cont.
Classification Results for cases not selected for use in the analysis (holdout sample) Actual Group Group Group 1 2
Predicted Group Membership No. of Cases 1
6 6 4 66.7% 0 0.0%
2 2 33.3% 6 100.0%
Percent of grouped cases correctly classified: 83.33%.
Conducting Discriminant Analysis
?
Determine the Significance of Discriminant Function
?
?
The null hypothesis that, in the population, the means of all discriminant functions in all groups are ? equal can be statistically tested. In SPSS this test is based on Wilks‘ ? lambda. The significance level is estimated based on a chi-square test. If the null hypothesis is rejected, indicating significant discrimination, one can proceed to interpret the results.
Conducting Discriminant Analysis
Interpret the Results
?
The interpretation of the discriminant weights, or coefficients, is similar to that in multiple regression analysis. The relative importance of the variables is seen from the absolute magnitude of the standardized discriminant function coefficients or the structure correlations, also called canonical loadings or discriminant loadings. These simple correlations between each predictor and the discriminant function represent the variance that the predictor shares with the function. Another aid to interpreting discriminant analysis results is to develop a characteristic profile for each group by describing each group in terms of the group means for the predictor variables.
?
?
?
Conducting Discriminant Analysis
Access Validity of Discriminant Analysis
?
The discriminant weights, estimated by using the analysis sample, are multiplied by the values of the predictor variables in the holdout sample to generate discriminant scores for the cases in the holdout sample. The cases are then assigned to groups based on their discriminant scores and an appropriate decision rule. The hit ratio, or the percentage of cases correctly classified, can then be determined by summing the diagonal elements and dividing by the total number of cases.
?
?
Stepwise Discriminant Analysis
?
?
Stepwise discriminant analysis is similar to stepwise multiple regression in that the predictors are entered sequentially based on their ability to discriminate between the groups. An F ratio is calculated for each predictor variable.
?
The predictor with the highest F ratio is the first to be included in the discriminant function.
A second predictor is added based on the highest adjusted or partial F ratio, taking into account the predictor already selected.
?
SPSS Windows
The DISCRIMINANT program performs both twogroup and multiple discriminant analysis. To select this procedure using SPSS for Windows click: Analyze>Classify>Discriminant …
doc_844755249.ppt
This is a ppt consists of discrimminant analysis concepts.
Discrimminant Analysis
Similarities and Differences between ANOVA, Regression, and Discriminant Analysis
Table 1
ANOVA REGRESSION One DISCRIMINANT ANALYSIS One
Similarities Number of dependent variables Number of independent variables
Differences Nature of the dependent variables Nature of the independent variables
One
Multiple
Multiple
Multiple
Metric Categorical
Metric Metric
Categorical Metric
Discriminant Analysis
Discriminant analysis is a technique for analyzing data when the criterion or dependent variable is categorical and the predictor or independent variables are interval in nature. The objectives of discriminant analysis are as follows: ? Development of discriminant functions, or linear combinations of the predictor or independent variables, which will best discriminate between the categories of the criterion or dependent variable (groups). ? Examination of whether significant differences exist among the groups, in terms of the predictor variables. ? Determination of which predictor variables contribute to most of the intergroup differences. ? Classification of cases to one of the groups based on the values of the predictor variables. ? Evaluation of the accuracy of classification.
Discriminant Analysis
?
?
?
?
When the criterion variable has two categories, the technique is known as two-group discriminant analysis. When three or more categories are involved, the technique is referred to as multiple discriminant analysis. The main distinction is that, in the two-group case, it is possible to derive only one discriminant function. The first function has the highest ratio of between-groups to within-groups sum of squares. The second function, uncorrelated with the first, has the second highest ratio, and so on. However, not all the functions may be statistically significant.
Discriminant Analysis Model
The discriminant analysis model involves linear combinations of the following form:
D = b0 + b1X1 + b2X2 + b3X3 + . . . + bkXk
where
D b 's X 's
?
= = =
discriminant score discriminant coefficient or weight predictor or independent variable
?
The coefficients, or weights (b), are estimated so that the groups differ as much as possible on the values of the discriminant function. This occurs when the ratio of between-group sum of squares to within-group sum of squares for the discriminant scores is at a maximum.
Statistics Associated with Discriminant Analysis
?
?
?
Canonical correlation. Canonical correlation measures the extent of association between the discriminant scores and the groups. Centroid. The centroid is the mean values for the discriminant scores for a particular group. There are as many centroids as there are groups. The means for a group on all the functions are the group centroids. Classification matrix. the classification matrix contains the number of correctly classified and misclassified cases.
Statistics Associated with Discriminant Analysis
?
?
?
Discriminant function coefficients. The discriminant function coefficients (unstandardized) are the multipliers of variables, when the variables are in the original units of measurement. Discriminant scores. The unstandardized coefficients are multiplied by the values of the variables. These products are summed and added to the constant term to obtain the discriminant scores. Eigenvalue. For each discriminant function, the Eigenvalue is the ratio of between-group to withingroup sums of squares. Large Eigenvalues imply superior functions.
Statistics Associated with Discriminant Analysis
?
F values and their significance. These are
?
?
calculated from a one-way ANOVA, with the grouping variable serving as the categorical independent variable. Each predictor, in turn, serves as the metric dependent variable in the ANOVA. Group means and group standard deviations. These are computed for each predictor for each group. Pooled within-group correlation matrix. The pooled within-group correlation matrix is computed by averaging the separate covariance matrices for all the groups.
Statistics Associated with Discriminant Analysis
?
?
?
?
Standardized discriminant function coefficients. These are the discriminant function coefficients and are used as the multipliers when the variables have been standardized to a mean of 0 and a variance of 1. Structure correlations. Also referred to as discriminant loadings, the structure correlations represent the simple correlations between the predictors and the discriminant function. Total correlation matrix. If the cases are treated as if they were from a single sample and the correlations computed, a total correlation matrix is obtained. Wilks' . Sometimes also called the U statistic, Wilks' for each predictor is the ratio of the within-group sum of squares to ? ? the total sum of squares. Its value varies between 0 and 1. Large values of (near 1) indicate that group means do not seem to be different. Small values of (near 0) indicate that ? the group means seem to be different.?
Conducting Discriminant Analysis
Fig. 1
Formulate the Problem
Estimate the Discriminant Function Coefficients
Determine the Significance of the Discriminant Function
Interpret the Results
Assess Validity of Discriminant Analysis
Conducting Discriminant Analysis
Formulate the Problem
?
?
?
?
?
?
Identify the objectives, the criterion variable, and the independent variables. The criterion variable must consist of two or more mutually exclusive and collectively exhaustive categories. The predictor variables should be selected based on a theoretical model or previous research, or the experience of the researcher. One part of the sample, called the estimation or analysis sample, is used for estimation of the discriminant function. The other part, called the holdout or validation sample, is reserved for validating the discriminant function. Often the distribution of the number of cases in the analysis and validation samples follows the distribution in the total sample.
Information on Resort Visits: Analysis Sample
Table 2
Resort Visit Annual Family Income ($000) Attitude Toward Travel Importance Household Age of Attached Size Head of to Family Household Vacation Amount Spent on Family Vacation
No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
50.2 70.3 62.9 48.5 52.7 75.0 46.2 57.0 64.1 68.1 73.4 71.9 56.2 49.3 62.0
5 6 7 7 6 8 5 2 7 7 6 5 1 4 5
8 7 5 5 6 7 3 4 5 6 7 8 8 2 6
3 4 6 5 4 5 3 6 4 5 5 4 6 3 2
43 61 52 36 55 68 62 51 57 45 44 64 54 56 58
M (2) H (3) H (3) L (1) H (3) H (3) M (2) M (2) H (3) H (3) H (3) H (3) M (2) H (3) H (3)
Information on Resort Visits: Analysis Sample
Table 2 cont.
Resort Visit 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Annual Family Income ($000) 32.1 36.2 43.2 50.4 44.1 38.3 55.0 46.1 35.0 37.3 41.8 57.0 33.4 37.5 41.3 Attitude Toward Travel 5 4 2 5 6 6 1 3 6 2 5 8 6 3 3 Importance Household Age of Attached Size Head of to Family Household Vacation 4 3 5 2 6 6 2 5 4 7 1 3 8 2 3 3 2 2 4 3 2 2 3 5 4 3 2 2 3 2 58 55 57 37 42 45 57 51 64 54 56 36 50 48 42 Amount Spent on Family Vacation L L M M M L M L L L M M L L L (1) (1) (2) (2) (2) (1) (2) (1) (1) (1) (2) (2) (1) (1) (1)
No.
16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
Information on Resort Visits: Holdout Sample
Table 3
Resort Visit Annual Family Income ($000) Attitude Toward Travel Importance Household Age of Attached Size Head of to Family Household Vacation Amount Spent on Family Vacation
No.
1 2 3 4 5 6 7 8 9 10 11 12
1 1 1 1 1 1 2 2 2 2 2 2
50.8 63.6 54.0 45.0 68.0 62.1 35.0 49.6 39.4 37.0 54.5 38.2
4 7 6 5 6 5 4 5 6 2 7 2
7 4 7 4 6 6 3 3 5 6 3 2
3 7 4 3 6 3 4 5 3 5 3 3
45 55 58 60 46 56 54 39 44 51 37 49
M(2) H (3) M(2) M(2) H (3) H (3) L (1) L (1) H (3) L (1) M(2) L (1)
Conducting Discriminant Analysis
Estimate the Discriminant Function Coefficients
The direct method involves estimating the discriminant function so that all the predictors are included simultaneously. In stepwise discriminant analysis, the predictor variables are entered sequentially, based on their ability to discriminate among groups.
?
?
Results of Two-Group Discriminant Analysis
Table 4
GROUP MEANS VISIT 1 2 Total
INCOME
60.52000 41.91333 51.21667
TRAVEL VACATION
5.40000 4.33333 4.86667 5.80000 4.06667 4.9333
HSIZE
4.33333 2.80000 3.56667
AGE
53.73333 50.13333 51.93333
Group Standard Deviations 1 2 Total 9.83065 7.55115 12.79523 1.91982 1.95180 1.97804 1.82052 2.05171 2.09981 1.23443 .94112 1.33089 HSIZE 8.77062 8.27101 8.57395 AGE
Pooled Within-Groups Correlation Matrix INCOME TRAVEL VACATION INCOME TRAVEL VACATION HSIZE AGE 1.00000 0.19745 0.09148 0.08887 - 0.01431 1.00000 0.08434 -0.01681 -0.19709
1.00000 0.07046 0.01742
1.00000 -0.04301
1.00000
Wilks' (U-statistic) and univariate F ratio with 1 and 28 degrees of freedom Variable INCOME TRAVEL VACATION HSIZE AGE Wilks' 0.45310 0.92479 0.82377 0.65672 0.95441 F 33.800 2.277 5.990 14.640 1.338 Significance 0.0000 0.1425 0.0209 0.0007 0.2572
Contd.
Results of Two-Group Discriminant Analysis
Table 4 cont.
CANONICAL DISCRIMINANT FUNCTIONS Function Eigenvalue % of Variance Cum Canonical After Wilks' % Correlation Function ? : 0 0 .3589 100.00 0.8007 : Chi-square df Significance 26.130 5 0.0001
1*
1.7862
100.00
* marks the 1 canonical discriminant functions remaining in the analysis. Standard Canonical Discriminant Function Coefficients FUNC INCOME TRAVEL VACATION HSIZE AGE 1
0.74301 0.09611 0.23329 0.46911 0.20922
Structure Matrix: Pooled within-groups correlations between discriminating variables & canonical discriminant functions (variables ordered by size of correlation within function)
FUNC
INCOME HSIZE VACATION TRAVEL AGE
1
0.82202 0.54096 0.34607 0.21337 0.16354 Contd.
Results of Two-Group Discriminant Analysis
Table 4 cont.
Unstandardized Canonical Discriminant Function Coefficients INCOME TRAVEL VACATION HSIZE AGE (constant) FUNC 1 0.8476710E-01 0.4964455E-01 0.1202813 0.4273893 0.2454380E-01 -7.975476 Canonical discriminant functions evaluated at group means (group centroids) Group 1 2 FUNC 1 1.29118 -1.29118
Classification results for cases selected for use in analysis Actual Group Group Group 1 2 Predicted No. of Cases 15 15 Group Membership 1 2 12 80.0% 0 0.0% 3 20.0% 15 100.0% Contd.
Percent of grouped cases correctly classified: 90.00%
Results of Two-Group Discriminant Analysis
Table 4 cont.
Classification Results for cases not selected for use in the analysis (holdout sample) Actual Group Group Group 1 2
Predicted Group Membership No. of Cases 1
6 6 4 66.7% 0 0.0%
2 2 33.3% 6 100.0%
Percent of grouped cases correctly classified: 83.33%.
Conducting Discriminant Analysis
?
Determine the Significance of Discriminant Function
?
?
The null hypothesis that, in the population, the means of all discriminant functions in all groups are ? equal can be statistically tested. In SPSS this test is based on Wilks‘ ? lambda. The significance level is estimated based on a chi-square test. If the null hypothesis is rejected, indicating significant discrimination, one can proceed to interpret the results.
Conducting Discriminant Analysis
Interpret the Results
?
The interpretation of the discriminant weights, or coefficients, is similar to that in multiple regression analysis. The relative importance of the variables is seen from the absolute magnitude of the standardized discriminant function coefficients or the structure correlations, also called canonical loadings or discriminant loadings. These simple correlations between each predictor and the discriminant function represent the variance that the predictor shares with the function. Another aid to interpreting discriminant analysis results is to develop a characteristic profile for each group by describing each group in terms of the group means for the predictor variables.
?
?
?
Conducting Discriminant Analysis
Access Validity of Discriminant Analysis
?
The discriminant weights, estimated by using the analysis sample, are multiplied by the values of the predictor variables in the holdout sample to generate discriminant scores for the cases in the holdout sample. The cases are then assigned to groups based on their discriminant scores and an appropriate decision rule. The hit ratio, or the percentage of cases correctly classified, can then be determined by summing the diagonal elements and dividing by the total number of cases.
?
?
Stepwise Discriminant Analysis
?
?
Stepwise discriminant analysis is similar to stepwise multiple regression in that the predictors are entered sequentially based on their ability to discriminate between the groups. An F ratio is calculated for each predictor variable.
?
The predictor with the highest F ratio is the first to be included in the discriminant function.
A second predictor is added based on the highest adjusted or partial F ratio, taking into account the predictor already selected.
?
SPSS Windows
The DISCRIMINANT program performs both twogroup and multiple discriminant analysis. To select this procedure using SPSS for Windows click: Analyze>Classify>Discriminant …
doc_844755249.ppt