Last chance! 50% off unlimited learning
Sale ends in
Produces SPSS- and SAS-like output for linear discriminant function analysis.
DFA(data, groups, variables, plot, predictive, priorprob, covmat_type, CV, verbose)If verbose = TRUE, the displayed output includes descriptive statistics for the groups, tests of univariate and multivariate normality, the results of tests of the homogeneity of the group variance-covariance matrices, eigenvalues & canonical correlations, Wilks lambda & peel-down statistics, raw and standardized discriminant function coefficients, structure coefficients, functions at group centroids, one-way ANOVA tests of group differences in scores on each discriminant function, one-way ANOVA tests of group differences in scores on each original DV, significance tests for group differences on the original DVs according to Bird et al. (2014), a plot of the group means on the standardized discriminant functions, and extensive output from predictive discriminant function analyses (if requested).
The returned output is a list with elements
canonical discriminant function coefficients
structure coefficients
standardized coefficients
standardized coefficients from SPSS
unstandardized canonical discriminant functions evaluated at the group means
group standard deviations on the unstandardized functions
standardized canonical discriminant functions evaluated at the group means
group standard deviations on the standardized functions
scores on the discriminant functions
One-way ANOVAs using the scores on a discriminant function as the DV
One-way ANOVAs on the original DVs
Significance tests when controlling the MFWER by (only) carrying out multiple t tests
Significance tests for the two-stage approach to controling the MFWER
The predicted group classifications
The posterior probabilities for the predicted group classifications
Cross-tabulation of the original and predicted group memberships
Proportion of original grouped cases correctly classified
Chi-square test of independence
Press's Q significance test of classifiation accuracy for original vs. predicted group memberships
Row Frequencies
Column Frequencies
Cell Proportions
Row-Based Proportions
Column-Based Proportions
Agreement (kappas) between the predicted and original group memberships
Classifications from leave-one-out cross-validations
Cross-Tabulation of the cross-validated and predicted group memberships
Proportion of cross-validated grouped cases correctly classified
Chi-square test of indepedence
Press's Q significance test of classifiation accuracy for cross-validated vs. predicted group memberships
Row frequencies
Column frequencies
Cell proportions
Row-based proportions
Column-based proportions
Agreement (kappas) between the cross-validated and original group memberships
Agreement (kappas) between the cross-validated and predicted group memberships
A dataframe where the rows are cases & the columns are the variables.
The name of the groups variable in the dataframe,
e.g., groups = 'Group'.
The names of the continuous variables in the dataframe that will be used in the DFA,
e.g., variables = c('varA', 'varB', 'varC').
Should a plot of the mean standardized discriminant function scores
for the groups be produced? The options are: TRUE (default) or FALSE.
Should a predictive DFA be conducted?
The options are: TRUE (default) or FALSE.
If predictive = TRUE, how should the prior probabilities of the group sizes be computed?
The options are:
'EQUAL' for equal group sizes; or
'SIZES' (default) for the group sizes to be based on the sizes of the groups in the dataframe.
The kind of covariance to be used for a predictive DFA. The options are:
'within' (for the pooled within-groups covariance matrix, which is the default) or
'separate' (for separate-groups covariance matrices).
If predictive = TRUE, should cross-validation (leave-one-out cross-validation) analyses also be conducted?
The options are: TRUE (default) or FALSE.
Should detailed results be displayed in console?
The options are: TRUE (default) or FALSE.
Brian P. O'Connor
The predictive DFA option using separate-groups covariance matrices (which is often called 'quadratic DFA') is conducted following the procedures described by Rencher (2002). The covariance matrices in this case are based on the scores on the continuous variables. In contrast, the 'separate-groups' option in SPSS involves use of the group scores on the discriminant functions (not the original continuous variables), which can produce different classifications.
See the documentation below for the GROUP.DIFFS function for information on the interpretation of the Bayes factors and effect sizes that are produced for the group comparisons.
Bird, K. D., & Hadzi-Pavlovic, D. (2013). Controlling the maximum familywise Type I error
rate in analyses of multivariate experiments. Psychological Methods, 19(2), p. 265-280.
Manly, B. F. J., & Alberto, J. A. (2017). Multivariate statistical methods:
A primer (4th Edition). Chapman & Hall/CRC, Boca Raton, FL.
Rencher, A. C. (2002). Methods of Multivariate Analysis (2nd ed.). New York, NY: John Wiley & Sons.
Sherry, A. (2006). Discriminant analysis in counseling research. Counseling Psychologist, 34, 661-683.
Tabachnik, B. G., & Fidell, L. S. (2019). Using multivariate statistics (7th ed.). New York, NY: Pearson.
DFA_Field=DFA(data = data_DFA_Field,
groups = 'Group',
variables = c('Actions','Thoughts'),
predictive = TRUE, priorprob = 'SIZES',
covmat_type='separate', # altho better to used 'separate' for these data
verbose = TRUE)
# \donttest{
# plots of posterior probabilities by group
# hoping to see correct separations between cases from different groups
# first, display the posterior probabilities
print(cbind(round(DFA_Field$posteriors[1:3],3), DFA_Field$posteriors[4]))
# group NT vs CBT
plot(DFA_Field$posteriors$posterior_NT, DFA_Field$posteriors$posterior_CBT,
pch = 16, col = c('red', 'blue', 'green')[DFA_Field$posteriors$Group],
xlim=c(0,1), ylim=c(0,1),
main = 'DFA Posterior Probabilities by Original Group Memberships',
xlab='Posterior Probability of Being in Group NT',
ylab='Posterior Probability of Being in Group CBT' )
legend(x=.8, y=.99, c('CBT','BT','NT'), cex=1.2, col=c('red', 'blue', 'green'), pch=16, bty='n')
# group NT vs BT
plot(DFA_Field$posteriors$posterior_NT, DFA_Field$posteriors$posterior_BT,
pch = 16, col = c('red', 'blue', 'green')[DFA_Field$posteriors$Group],
xlim=c(0,1), ylim=c(0,1),
main = 'DFA Posterior Probabilities by Group Membership',
xlab='Posterior Probability of Being in Group NT',
ylab='Posterior Probability of Being in Group BT' )
legend(x=.8, y=.99, c('CBT','BT','NT'), cex=1.2,col=c('red', 'blue', 'green'), pch=16, bty='n')
# group CBT vs BT
plot(DFA_Field$posteriors$posterior_CBT, DFA_Field$posteriors$posterior_BT,
pch = 16, col = c('red', 'blue', 'green')[DFA_Field$posteriors$Group],
xlim=c(0,1), ylim=c(0,1),
main = 'DFA Posterior Probabilities by Group Membership',
xlab='Posterior Probability of Being in Group CBT',
ylab='Posterior Probability of Being in Group BT' )
legend(x=.8, y=.99, c('CBT','BT','NT'), cex=1.2, col=c('red', 'blue', 'green'), pch=16, bty='n')
DFA_Sherry <- DFA(data = data_DFA_Sherry,
groups = 'Group',
variables = c('Neuroticism','Extroversion','Openness',
'Agreeableness','Conscientiousness'),
predictive = TRUE, priorprob = 'SIZES',
covmat_type='separate',
verbose = TRUE)
# plots of posterior probabilities by group
# hoping to see correct separations between cases from different groups
# first, display the posterior probabilities
print(cbind(round(DFA_Sherry$posteriors[1:3],3), DFA_Sherry$posteriors[4]))
# group 1 vs 2
plot(DFA_Sherry$posteriors$posterior_1, DFA_Sherry$posteriors$posterior_2,
pch = 16, cex = 1, col = c('red', 'blue', 'green')[DFA_Sherry$posteriors$Group],
xlim=c(0,1), ylim=c(0,1),
main = 'DFA Posterior Probabilities by Original Group Memberships',
xlab='Posterior Probability of Being in Group 1',
ylab='Posterior Probability of Being in Group 2' )
legend(x=.8, y=.99, c('1','2','3'), cex=1.2, col=c('red', 'blue', 'green'), pch=16, bty='n')
# group 1 vs 3
plot(DFA_Sherry$posteriors$posterior_1, DFA_Sherry$posteriors$posterior_3,
pch = 16, col = c('red', 'blue', 'green')[DFA_Sherry$posteriors$Group],
xlim=c(0,1), ylim=c(0,1),
main = 'DFA Posterior Probabilities by Group Membership',
xlab='Posterior Probability of Being in Group 1',
ylab='Posterior Probability of Being in Group 3' )
legend(x=.8, y=.99, c('1','2','3'), cex=1.2,col=c('red', 'blue', 'green'), pch=16, bty='n')
# group 2 vs 3
plot(DFA_Sherry$posteriors$posterior_2, DFA_Sherry$posteriors$posterior_3,
pch = 16, col = c('red', 'blue', 'green')[DFA_Sherry$posteriors$Group],
xlim=c(0,1), ylim=c(0,1),
main = 'DFA Posterior Probabilities by Group Membership',
xlab='Posterior Probability of Being in Group 2',
ylab='Posterior Probability of Being in Group 3' )
legend(x=.8, y=.99, c('1','2','3'), cex=1.2, col=c('red', 'blue', 'green'), pch=16, bty='n')
# data from Tabachnik & Fiddel (2019, p 307)
table9.1 <- '
1 87 5 31 6.4
1 97 7 36 8.3
1 112 9 42 7.2
2 102 16 45 7.0
2 85 10 38 7.6
2 76 9 32 6.2
3 120 12 30 8.4
3 85 8 28 6.3
3 99 9 27 8.2'
table9.1 <- data.frame(read.table(text=table9.1,
col.names=c('group','perf','info','verbexp','age')))
DFA(data = table9.1,
groups = 'group',
variables = c('perf','info','verbexp','age'),
predictive = TRUE, priorprob = 'SIZES', covmat_type='within',
verbose = TRUE)
# }
Run the code above in your browser using DataLab