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22 Cards in this Set
- Front
- Back
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Multivariate Data Analysis
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statistical methods that allow the simultaneous investigation of more than two variables. There are two basic groups of multivariate data analysis procedures; Analysis of Dependence and Analysis of Interdependence
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Analysis of Dependence
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a collective term to describe any multivariate statistical technique that attempts to explain or predict one or more dependent variables on the basis of two or more independent variables.
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Analysis of Interdependence
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a collective term used to describe any multivariate statistical technique that attempts to give meaning to a set of variables or seeks to group things together.
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Influence of Measurement Scales
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as with other statistical techniques the nature of the measurement scales will determine which multivariate technique is appropriate for the data. The choice of technique is determined by two issues
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Multiple regression analysis
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an analysis of association in which the effects or two or more independent variables on a single interval- or ratio-scaled dependent variable are investigated simultaneously.
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Coefficient of partial regression
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the percentage of the variance in the dependent variable which is explained by a single independent variable, with the other variables held constant.
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Coefficient of multiple determination
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in multiple regression the percentage of variance in the dependent variable that is explained by the variation in the independent variables
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Test of the significance of the coefficient of determination
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the F-test is used to test the relative magnitudes of the sum of squares due to the regression (SSr), and the error sum of squares (SSe) with the appropriate degrees of freedom
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Multiple discriminant analysis
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a statistical technique for predicting the probability that an object will belong in one of two or more mutually exclusive categories—the nomially scaled dependent variable, based on 2 or more independent variables.
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Confusion matrix
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a four-celled table that compares predicted and actual placement of objects and shows the number of successful and unsuccessful predictions based on use of the multiple discriminant function.
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Canonical correlation
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technique used to determine the degree of linear association between two sets of variables, contains both 2 or more independent and dependent variables both of which scaled on either an interval or ratio scale
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Factor Analysis
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used to discern the underlying dimensions or regularity in phenomena—general purpose is to summarize the information contained in a large number of variables into a smaller number of factors.
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Multivariate Analysis of Variance
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Is used to determine significance of differences between means with 2 or more interval or ratio scaled dependent variables and 1 or more nominally scaled independent variables
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Factor loading
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measure of the importance of a variable in explaining a factor
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Factor score
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numbers that represent each observation’s calculated value on each factor in a factor analysis. The factor score is an individual’s combined response to the several variables representing the factor.
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Communality
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how much a variable has in common with all factors—a measure of the percentage of a variable’s variation explained by the factors. High communality means the variable has much in common with the variables of the other factors.
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Rotation
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a factor analysis may have several solutions depending upon the type of rotation. Geometrically this corresponds to how the X and Y axes are rotated and the effect of the rotation on the various correlational scatterplots. The technical aspects of factor rotation are beyond the scope of this text and course.
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Cluster analysis
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classifies individuals or objects into a small number of mutually exclusive groups such that there will be as much likeness within groups and as much differentiation among groups as possible
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Difference between factor analysis and cluster analysis
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the purpose of factor analysis is to search for constructs underlying variables (population, retail sales, sales outlets, etc.)
and the purpose of Cluster analysis is to search for constructs underlying objects (cities, individuals, industries, etc.) |
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Difference between multiple discriminant analysis and cluster analysis
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In Multiple discriminant analysis the groups are predetermined (successful versus on successful sales reps, banks that remain solvent versus banks that fail, etc.) and in Cluster analysis the groups are not predetermined—the purpose of the cluster analysis is to find out what groups are out there.
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Multidimensional scaling
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measures attitudes about objects in multidimensional space on the basis of respondents’ judgments of similarity of objects—the perceptual difference among objects is reflected in the relative distance between objects in multidimensional space.
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Chi-square automatic interaction detection (CHAID)
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a clustering method used to investigate the interaction of a large set of independent variables—a way of breaking a large heterogeneous group into various homogeneous groups. Investigates the relationship between a dependent variable and a series of predictor variables. The objective is to form subgroups through a number of sequentially generated binary splits
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