Section 3: Rummel: 33. R. J. Rummel (1967, p. 451+) discusses the application of factor analysis for "induction" AND "deduction" (as opposed to VERSUS). Select one of the research articles in the required readings to characterize each of these applications and explain how each typifies the approach. Gould 9. Johnson and Brunn ("Residential Preference Patterns of Afro-American College Students in Three Different States") and Gould ("Problems of Space Preference Measures and Relationships") were concerned with the construction of "mental maps". Describe this process. 103. Wong 20. Wong used principal components analysis to extract the underlying dimensions of New England watershed characteristics (drainage area, basin shape, main channel slope, tributary channel slope, percent of the area in ponds and lakes, average land slope, mean altitude, length of longest water course,length of main stream, stream density, frequency and intensity of precipitation, and mean annual flood). Briefly discuss the two dominant components extracted by Wong and the primary criticisms levelled by Court. 56. Court leveled several criticisms at Wong's work. What were the major criticisms Court presented and how did Wong respond to them? Johnson and Brunn 9. (see Gould above) Henshall and King 12. Johnston ("Classification in Geography") and Henshall and King ("...Peasant Agriculture in Barbados") utilize an elementary statistical tool to accomplish rather sophisticated tasks. Compare the uses of this tool in the two articles. 43. Several articles discussed in class and/or read used unusual data or similarities matrices for factor/components analysis. Briefly describe the unusual aspects of the following: a. Pigozzi, unemployment time series analysis b. A. Holsman, "Higher-Order Factor Analysis..." c. Henshall and King, "...Peasant Agriculture in Barbados d. Wm. Black, "Toward a Factorial Ecology of Flows" 57. Henshall and King use a components analysis on an unusual data set. Explain the unusual aspects of their analysis. Black 43. (see Henshall and King above) 52. William R. Black, in an article titled "Toward a Factorial Ecology of Flows," performs a components analysis on an unusual data set. Explain the nature of the data set, the resulting components, and scores. Riddell 24. Explain the series of steps conducted by Riddell in producing "reconstituted regression coefficients" and explain the limitations of this technique with specific reference to Hauser's comments. 34. One reason for doing Factor/Component Analyses is to develop independent variables for regression. Explain how this is accomplished and how "reconstituted regression coefficients" may be developed. The Riddell article is an example you might want to integrate into your answer. Bagchi-Sen and Pigozzi Holsman 43. (see Henshall and King above) Wyly Section 4 AAG 28. The Abler, Adams, and Gould chapter "Classification" describes an analysis of households, housing and other characterisics of urban census tracts. Describe the major dimensions of variation and how they are used to establish neighborhoods. 61. Abler, Adams and Gould present three bases for combining elements in a sequential grouping situation (simple linkage, average linkage, and complete linkage); describe and contrast these three bases. Lapointe King McConnell 14. In many respects James McConnell's article "The Export Decision: An Empirical Study of Firm Behavior" is an example of nearly all the methods studied this term. Discuss the sequential application of methodologies in this article. 100. In many respects James McConnell's article "The Export Decision: An Empirical Study of Firm Behavior" and the Biles/Pigozzi paper “The Interaction of Economic Reforms, Socio-economic Structure and Agriculture in Mexico” are both examples of nearly all the methods studied this semester. Discuss the sequential application of methodologies in ONE of these articles. Biles and Pigozzi 92. Biles & Pigozzi (2000) use several techniques presented in the second part of the course; explain these applications. 100. (see McConnell) Stynes and Pigozzi 59. The following equation is the basis of a harmonic analysis, like the one done by Stynes and Pigozzi. Using this notation as a base, summarize the harmonic results of the Stynes & Pigozzi paper. EMBED Equation By Topic PCA 11. Briefly discuss four "rules" for selecting the number of factors to extract in a common factor or principal components analysis. 13. There are two basic "indeterminancies" in common factor analysis; the number of factors and the communalities. How are the final communalities determined in FACTOR ANALYSIS? 22. Factor/principal components analysis (FA/PC) is often used to explore for some underlying structure. Select three (3) of the articles read this term and discuss how FA/PC was used as an exploratory tool. 33. (see Rummel) 34. (see Riddell) 35. (see also 89) Three "slices" of a data block present 6 "modes" of Factor/Components Analysis. Briefly define these and indicate the nature of the results (therefore the application) for each. 43. (see Henshall and King) 48. One method for determining the number of components to extract and rotate in a components anaylsis is to incorporate a vector of random numbers. Explain how and why this technique works. 49. In a components analysis, what are the relationships between the communalities, percentage of the variance, and the eigenvalues. How are these relationships affected by rotation? 52. (see Black) 84. Describe what will be the results of using a correlation matrix and then a covariance matrix in PCA. What will the differences be? What will the similarities be? How are these dependent upon the data used? 89. . (see also35) Three "slices" of a data block presented 6 "modes" of Factor/Components Analysis. Briefly define the Q-R slice (hence, Q and R modes), and indicate the nature of the results (therefore the application) for each. 103. Reconstitution 24. (see Riddell) 34. (see Riddell) 50. When one does a regression on component scores it is possible to "reconstitute" the regression coefficients so as to reveal how the original variables participate in a linear relationship. Explain the mathematical relationships involved in this process. 60. In the following equations, utilized in the reconstitution of regression coefficients process, S represents "scores," Z represents "standardized data," Y is a dependent variable, B and C are vectors of regression coefficients. Explain the reconstitution process by completing the mathematical equations and describe the content of the operations you perform inorder to reach the "reconstituted" coefficients. What are the "reconstituted" coefficients? EMBED Equation EMBED Equation EMBED Equation Q-mode 19. Briefly describe a situation where a Q-mode factor analysis might prove useful. Provide sufficient detail by noting what factors might emerge from your original data. How does this differ from other modes? 51. Explain the difference between an R-mode and a Q-mode components analysis. Be certain to include the advantages and limitations of one compared to the other. 89. (see PCA) Discriminant Analysis 75. Discriminant Analysis is based on the equation: EMBED Equation.3 What are B and W, what is their construction, and how are they related? 90. Analyses involving binary variables or outcomes, conceptually comparable to "discriminant analysis," were presented in class: a) logit regression designs and b) neural network models. Dscribe either a) or b). Grouping 5. Factor scores are often used in hierarchical grouping methods. What characteristic(s) of these scores makes them useful in this process and how are they used? 14. (see McConnell) 53. Hierarchical grouping proceeds by linking observation which are closest together. This is done using a distance matrix which can be derrived through a components analysis. Explain how this distance matrix is produced. 55. Components analysis can be used in grouping. Compare and contrast the groups which result from a Q-mode components analysis and from hierarchical grouping methods using scores of an R-mode analysis. 61. (see AAG above) 76 The incremental F-test was proposed as an aid in the selection of the number of groups to entertain in a grouping process. Explain how it can be used. 91. There is a very common problem troubling classification/grouping schema: correlated variables used to "group" observations. Explain why this is a problem and how one might fix it. Harmonic Analysis 54. Given the function: EMBED Equation Describe, using this notation and verbal description, the frequency, amplitude, and phase angle as used in a harmonic analysis. SYSTAT 41. Given the following portions of SYSTAT printout compute and identify the meaning or significance of each of a through e, for both the unrotated and rotated solution. a) a12 b) ((Llambda 2) c) h32 d) % of total variance, dimension #1 e) % of common variance, dimension #1 ---------------------------------- COMPONENT LOADINGS 1 2 DISTANCE .923 -.316 DENSITY -.779 .598 INCOME .771 .496 SCHOOL .746 .501 ROTATED LOADINGS 1 2 DENSITY -.977 -.107 DISTANCE .885 .410 INCOME .213 .891 SCHOOL .194 .880 102. Given the following portions of SYSTAT printout compute (where necessary) and identify the meaning or significance of each of a through e, for both the unrotated and rotated solution. a) a12 b) (2(Llambda 2) c) h32 d) % of total variance, dimension #1 e) % of common variance, dimension #1 ---------------------------------- LATENT ROOTS 1 2 3 4 1.853 1.103 0.724 0.320 COMPONENT LOADINGS 1 2 V1 .832 .367 V2 .673 -.164 V3 -.835 .107 V4 .109 -.964 ROTATED LOADINGS 1 2 V1 .846 .332 V2 .665 -.192 V3 -.829 .142 V4 .069 -.968