Description
It highlited the covers discriminant analysis in detail. Useful for understanding the basics for the marketing research course.
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Discriminant function analysis - determine which variables discriminate between two or more naturally occurring groups. Dependent var – categorical ; independent variable – interval or metric Basic idea -to determine whether groups differ with regard to the mean of a variable, and then to use that variable to predict group membership (e.g., of new cases). Eg : Which variables discriminate between those who are credit card defaulters.(Age , marital status, lifestyle,…..). If one can build a model – credit card comp can a-prori ascertain high risk individuals and decide on membership
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What factors discriminates between Dell laptop users who will recommend Dell and those who will not. What factors – visit Burger King vs not What factors – buy EF jewellery vs not……..
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Depends on how many groups in dependent variable.
? A) Two Groups ? B) Multiple groups
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Two group : Similar to bivariate regression – interpretation similar (Fisher’s Linear Discriminant Analysis) If we recode Dependent var – as 1, 2 and run a regression , will get similar results as 2 group Discriminant. Fit a linear eqn : ( one discriminant function)
Group = a + b1x1 + b2x2 + ... + bmxm Variables with largest (standardized) regression coefficients are the ones that contribute most to the prediction of group membership.
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If 3 groups – 2 discriminant function. Function 1: Estimate for discriminating betw Group1 vs 2and 3 Function 2 : Estimate for discriminating between Group 2 vs Group3 Canonical Analysis : do not have to specify how to combine groups. Automatically determine optimal combination of variables – so the first function provides the most overall discrimination between groups, the second provides second most Functions orthogonal or independent Canonical correlation analysis will determine the successive functions and canonical roots (Eigenvalues =Betwn Group/Within Group Sum of
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Formulate the problem Estimate DF Coeff Sig of DF
Interpret results
Assess validity
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Categorical variable : Job Type : 1) customer service, 2) mechanic and 3) dispatcher Continuous variables : Outdoor , Social , Conservative An employer wants to know if these job types appeal to difft personality types. Administered qn on interest in above Objective : Assess relationship between the three continuous variables and categorical variable
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Mean s difft acros s grou ps Basis for
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If predictors are strongly correlated – shared impact on dep variable. Uncorrelated predictors preferred. Here, not strongly correlated.
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Eigenvalues – discriminating power of fn.( Ratio – BetwGrp to Within Grp variance; higher the better) . The groups shd differ as much as possible on the values of discriminant fn. Variance
iscriminating ability as a % - calculated as % eigenvalues. Canonical corr : How much each fn is useful in determining group membership. If zero – no relationship betwn groups& Dis fn . If 1 then perfectly discriminates between groups.
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Score1 = 0.379*zoutdoor - 0.831*zsocial + 0.517*zconservative Score2 = 0.926*zoutdoor + 0.213*zsocial - 0.291*zconservative ? Each resp will have 2 scores .Distbn of scores have a mean =0 and SD=1. ? Magnitude of coeff indicates how strongly it affects the score.
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Standardized Canonical Discriminant Function Coefficients . Coeff used to calculate Discriminant scores. If zoutdoor , zsocial and zconservative are 3 variables,
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Each respondent ( with 2 scores on each function ) will belong to a job cat. We can calculate the Discriminant score for all samples in each group using Discriminant coeff . The mean of those scores is the Group Centroids
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Fn 1 has a large coeff on conservative and a large negative on social. (Positively discriminates on Conservative and negatively on Social). Attitude is conservative , but less social Dispatch has the highest mean value on Function 1 , and Customer Service the lowest. This implies that those who tend to be conservative and less social would tend to have an affinity towards dispatch ( more solitary occupn), vis avis customer service. Fn2 has a large coeff on outdoor ; mechanics have the 14 highest value.
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The null hypotheses is that the canonical correlations associated with all functions=0. ( Functions have no discriminating ability.) Both functions are first tested simultaneously , and then the second function is tested. Wilks Lamda : Product of ( 1- cann corr sq ) of both fns. For the first function
1- 0.7212)*(1-0.4932) = 0.364 . For the second (10.4932) = 0.757. Lamda transforms into Chi sq statistic with d.o.f = (no of groups+no.of var) Here , both functions together , are sig ( <.05). When removed, second fn too is sig.
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We start off by assigning equal number of cases to each group.
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Predicted count
Sample count
Customer service had orginally 85 cases. Model predicted 89 cases - 70 were correctly classified (82.4%) ;12.9% misclassified as mechanic
19
doc_853182749.pptx
It highlited the covers discriminant analysis in detail. Useful for understanding the basics for the marketing research course.
1
?
? ?
?
Discriminant function analysis - determine which variables discriminate between two or more naturally occurring groups. Dependent var – categorical ; independent variable – interval or metric Basic idea -to determine whether groups differ with regard to the mean of a variable, and then to use that variable to predict group membership (e.g., of new cases). Eg : Which variables discriminate between those who are credit card defaulters.(Age , marital status, lifestyle,…..). If one can build a model – credit card comp can a-prori ascertain high risk individuals and decide on membership
2
?
? ?
What factors discriminates between Dell laptop users who will recommend Dell and those who will not. What factors – visit Burger King vs not What factors – buy EF jewellery vs not……..
3
?
Depends on how many groups in dependent variable.
? A) Two Groups ? B) Multiple groups
? ? ?
Two group : Similar to bivariate regression – interpretation similar (Fisher’s Linear Discriminant Analysis) If we recode Dependent var – as 1, 2 and run a regression , will get similar results as 2 group Discriminant. Fit a linear eqn : ( one discriminant function)
Group = a + b1x1 + b2x2 + ... + bmxm Variables with largest (standardized) regression coefficients are the ones that contribute most to the prediction of group membership.
4
? ?
?
?
?
? ?
If 3 groups – 2 discriminant function. Function 1: Estimate for discriminating betw Group1 vs 2and 3 Function 2 : Estimate for discriminating between Group 2 vs Group3 Canonical Analysis : do not have to specify how to combine groups. Automatically determine optimal combination of variables – so the first function provides the most overall discrimination between groups, the second provides second most Functions orthogonal or independent Canonical correlation analysis will determine the successive functions and canonical roots (Eigenvalues =Betwn Group/Within Group Sum of
5
Formulate the problem Estimate DF Coeff Sig of DF
Interpret results
Assess validity
6
? ? ?
Categorical variable : Job Type : 1) customer service, 2) mechanic and 3) dispatcher Continuous variables : Outdoor , Social , Conservative An employer wants to know if these job types appeal to difft personality types. Administered qn on interest in above Objective : Assess relationship between the three continuous variables and categorical variable
7
?
Mean s difft acros s grou ps Basis for
8
?
? ?
If predictors are strongly correlated – shared impact on dep variable. Uncorrelated predictors preferred. Here, not strongly correlated.
9
?
? ?
Eigenvalues – discriminating power of fn.( Ratio – BetwGrp to Within Grp variance; higher the better) . The groups shd differ as much as possible on the values of discriminant fn. Variance
iscriminating ability as a % - calculated as % eigenvalues. Canonical corr : How much each fn is useful in determining group membership. If zero – no relationship betwn groups& Dis fn . If 1 then perfectly discriminates between groups.10
?
?
Score1 = 0.379*zoutdoor - 0.831*zsocial + 0.517*zconservative Score2 = 0.926*zoutdoor + 0.213*zsocial - 0.291*zconservative ? Each resp will have 2 scores .Distbn of scores have a mean =0 and SD=1. ? Magnitude of coeff indicates how strongly it affects the score.
11
Standardized Canonical Discriminant Function Coefficients . Coeff used to calculate Discriminant scores. If zoutdoor , zsocial and zconservative are 3 variables,
?
?
Each respondent ( with 2 scores on each function ) will belong to a job cat. We can calculate the Discriminant score for all samples in each group using Discriminant coeff . The mean of those scores is the Group Centroids
13
?
?
?
Fn 1 has a large coeff on conservative and a large negative on social. (Positively discriminates on Conservative and negatively on Social). Attitude is conservative , but less social Dispatch has the highest mean value on Function 1 , and Customer Service the lowest. This implies that those who tend to be conservative and less social would tend to have an affinity towards dispatch ( more solitary occupn), vis avis customer service. Fn2 has a large coeff on outdoor ; mechanics have the 14 highest value.
15
? ? ?
? ?
The null hypotheses is that the canonical correlations associated with all functions=0. ( Functions have no discriminating ability.) Both functions are first tested simultaneously , and then the second function is tested. Wilks Lamda : Product of ( 1- cann corr sq ) of both fns. For the first function
1- 0.7212)*(1-0.4932) = 0.364 . For the second (10.4932) = 0.757. Lamda transforms into Chi sq statistic with d.o.f = (no of groups+no.of var) Here , both functions together , are sig ( <.05). When removed, second fn too is sig.16
17
?
We start off by assigning equal number of cases to each group.
18
Predicted count
Sample count
Customer service had orginally 85 cases. Model predicted 89 cases - 70 were correctly classified (82.4%) ;12.9% misclassified as mechanic
19
doc_853182749.pptx