Presentación de los avance de la tesis doctoral

1. Validation o f Order Rank Scales Based o n Compositional Data Analysis: A Proposal. Claudia Malpica Lander [email_address] Purificación Galindo Villardón [email_address] Universidad de Salamanca Departamento de Estadística

2. INTRODUCTION Validity Description and of order rank scales. Compositional data (AITCHISON, 1986) An application is presented in the management evaluation context.

3. LEADERSHIP DIMENSIONS BOLMAN AND DEAL (1991) STRUCTURAL HUMAN RESOURCE POLITICAL SYMBOLIC Roots: personality and social psychology Key concepts: needs (motives), capacities (skills), feelings Central focus: fit between individual and organization Roots: sociology, management science Key concepts: goals, roles (division of labor), formal relationships Central focus: alignment of structure with goals and environment Roots: political science Key concepts: interests, conflict, power, scarce resources Central focus: getting and using power, managing conflict to get things done Roots: social and cultural anthropology Key concepts: culture, myth, ritual, story, Central focus: building culture, staging organizational drama

4. CONSTRUCT VALIDITY OF LIKERT´S SCALE Validity 1.- Think very clearly and logically. 4 2.- Show high levels of support and concern for others. 5 3.- Have exceptional ability to mobilize people. 3 4.- Inspire others to do their best. 4 5.- Strongly emphasize careful planning and clear times lines. 4 … … … … … 31.- Succeed in the face of conflict and opposition. 5 32.- Serve as an influential model of organization aspirations and values. 3 1 = Never 2 = Occasionally 3 = Sometimes 4 = Often 5 = Always Exploratory and Confirmatory Factor Analysis 29 e29 1 1 25 e25 1 21 e21 1 17 e17 1 13 e13 1 i9 e9 1 5 e5 1 1 e1 1 29 e29 1 1 25 e25 1 21 e21 1 17 e17 1 13 e13 1 e9 1 5 e5 1 1 e1 1 i 30 e 30 1 1 2 6 e2 6 1 2 2 e2 2 1 1 8 e1 8 1 1 4 e1 4 1 i 10 e 10 1 i 6 e 6 1 i 2 e2 1 i 30 e 30 1 1 2 6 e2 6 1 2 2 e2 2 1 1 8 e1 8 1 1 4 e1 4 1 i 10 e 10 1 i 6 e 6 1 i 2 e2 1 i 31 e 31 1 1 2 7 e2 7 1 2 3 e2 3 1 1 9 e1 9 1 1 5 e15 1 i 11 e 11 1 i 7 e 7 1 i 3 e3 1 i 31 e 31 1 1 2 7 e2 7 1 2 3 e2 3 1 1 9 e1 9 1 1 5 e15 1 i 11 e 11 1 i 7 e 7 1 i 3 e3 1 i 31 e 31 1 1 2 7 e2 7 1 2 3 e2 3 1 1 9 e1 9 1 1 5 e15 1 i 11 e 11 1 i 7 e 7 1 i 3 e3 1 i 31 e 31 1 1 2 7 e2 7 1 2 3 e2 3 1 1 9 e1 9 1 1 5 e15 1 i 11 e 11 1 i 7 e 7 1 i 3 e3 1 STRUCTURAL HHRR POLITICAL SYMBOLIC

5. CONSTRUCT VALIDITY OF ORDER RANK SCALE Validity 1.- What has helped me the most to be successful is my ability to: ____A. Make good decisions. ____B. Coach and develop people. ____C. Build strong alliances. ____D. Energize and inspire others . … … … … … 6.- The best way to describe me is: ____A. Technical expert. ____B. Good listener. ____C. Skilled negotiator. ____D. Inspirational Leader . 2 3 1 4 4 1 2 3 4 = best describes 3 = next best … 1 = least like you Every question can be considered as a composition with total equal to 10 Validity A = STRUCTURAL B = HHRR C = POLITICAL D = SYMBOLIC Every dimension performes Laedership composition adding 60 Description

6. 360 - DEGREE FEEDBACK Validity Peers Supervisors Subordinates SELF Self (n = 1245) Supervisors (n = 1444) Peers (n = 2343) Subordinates (n = 2448) Ind1 Ind2 Indn 1A 1B 1C … 6D Mode 1: individuals Mode 2: Variables, Compositional Data Mode 3: Type of raters

7. COMPOSITIONAL DATA Validity Self Supervisors Peers Subordinates Ind1 Ind2 Ind3 Indn 1A 1B 1C . . . 6D BIPLOTS OF COMPOSITIONAL DATA Z=U  V T (GREENACRE & AITCHISON, 2002) Z  R D DOUBLE CENTRED l = log(x) x  S D x  S D AITCHISON´S DISTANCE (1992) CENTRED LOGRATIO, CLR Z  R D g(x) x log clr(x) z   (AITCHISON, 1986)

8. BIPLOT S OF COMPOSITIONAL DATA Validity -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1A 1B 1C 1D 2A 2B 2C 2D 3A 3B 3C 3D 4A 4B 4C 4D 5A 5B 5C 5D 6A 6B 6C 6D AXE 1 (17,75%) AXE 2 (14,22%) Political Symbolic Structural

9. BIPLOT S OF COMPOSITIONAL DATA Validity -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1A 1B 1C 1D 2A 2B 2C 2D 3A 3B 3C 3D 4A 4B 4C 4D 5A 5B 5C 5D 6A 6B 6C 6D AXE 1 (17,75%) AXE 3 (10,72%) HHRR POLITICAL SYMBOLIC

10. STATIS DUAL Validity Z 1 Z 2 Z K J I 1 I T I 2 INTER-STRUCTURE ANALYSIS COMPROMISE STRUCTURE INTRA-STRUCTURE ANALYSIS Z  R D DOUBLE CENTRED x  S D STATIS DUAL (LAVIT, 1988) S tructuration de T ableaux A T rois I ndices de la S tatistique (GREENACRE & AITCHISON, 2002)

11. STATIS DUAL Validity J J COMPROMISE STRUCTURE C 1 C 2 C k J J J J RV matrix K K C 2 C 4 C 1 C 3 INTER-STRUCTURE ANALYSIS PCA PCA J2_1 J1_1 J3_1 J1 _2 J2_2 J3_2 J2_3 J1_3 J3_3 J2_4 J1_4 J3_4 INTRA-STRUCTURE ANALYSIS J2_1 J1 J 2 J3 J4 J5 J6 J7 J8 J9 J1 0 J11

12. INTER-STRUCTURE ANALYSIS 0.241 0.258 0.252 0.248 Validity 0 1 2 3 4 5 6 7 8 -3 -2 -1 0 1 2 3 Self Supervisors Peers Subordinates

13. COMPROMISE STRUCTURE -15 -10 -5 0 5 10 15 20 -20 -15 -10 -5 0 5 10 15 1a 1b 1c 1d 2a 2b 2c 2d 3a 3b 3c 3d 4a 4b 4c 4d 5a 5b 5c 5d 6a 6b 6c 6d POLITICAL SYMBOLIC STRUCTURAL Validity

14. INTRA-STRUCTURE ANALYSIS (TRAYECTORIAS) Validity -20 -15 -10 -5 0 5 10 15 20 25 -25 -20 -15 -10 -5 0 5 10 15 20 1a 1c 1d 2a 2c 2d 3a 3b 3c 3d 4a 4b 4d 5a 5b 5c 6a 6b 6c 6d 1a_S 1c_S 1d_S 2a_S 2c_S 2d_S 3a_S 3c_S 3d_S 4a_S 4d_S 5c_S 6a_S 6b_S 6c_S 1a_U 1c_U 1d_U 2a_U 2c_U 2d_U 3a_U 3b_U 3c_U 3d_U 4a_U 4d_U 5a_U 5b_U 5c_U 6a_U 6b_U 6c_U 6d_U 1a_P 1c_P 1d_P 2a_P 2c_P 2d_P 3a_P 3b_P 3c_P 3d_P 4a_P 4b_P 4d_P 5a_P 5b_P 5c_P 6a_P 6b_P 6c_P 6d_P 1a_B 1c_B 1d_B 2a_B 2c_B 2d_B 3a_B 3b_B 3c_B 3d_B 4a_B 4b_B 4d_B 5a_B 5b_B 5c_B 6a_B 6b_B 6c_B 6d_B POLITICAL SYMBOLIC STRUCTURAL S elf (n = 1245) S U pervisors (n = 1444) P eers (n = 2343) Su B ordinates (n = 2448)

15. INTRA-STRUCTURE ANALYSIS (TRAYECTORIAS) Validity -20 -15 -10 -5 0 5 10 15 20 25 -20 -15 -10 -5 0 5 10 15 1a 1b 1c 1d 2a 2b 2c 2d 3a 3b 3c 3d 4a 4b 4c 4d 5b 5c 5d 6a 6b 6c 6d 1b_S 1c_S 1d_S 2a_S 2b_S 2c_S 2d_S 3b_S 3c_S 3d_S 4a_S 4b_S 4c_S 5b_S 5c_S 6b_S 6c_S 6d_S 1a_U 1b_U 1c_U 1d_U 2a_U 2b_U 2c_U 2d_U 3a_U 3b_U 3c_U 3d_U 4a_U 4b_U 4c_U 4d_U 5b_U 5c_U 5d_U 6b_U 6c_U 6d_U 1a_P 1b_P 1c_P 1d_P 2a_P 2b_P 2c_P 2d_P 3a_P 3b_P 3c_P 3d_P 4a_P 4b_P 4c_P 4d_P 5b_P 5c_P 5d_P 6a_P 6b_P 6c_P 6d_P 1a_B 1b_B 1c_B 1d_B 2a_B 2b_B 2c_B 2d_B 3a_B 3b_B 3c_B 3d_B 4a_B 4b_B 4c_B 4d_B 5b_B 5c_B 5d_B 6a_B 6b_B 6c_B 6d_B POLITICAL SYMBOLIC HHRR S elf (n = 1245) S U pervisors (n = 1444) P eers (n = 2343) Su B ordinates (n = 2448)

17. CONSIDERING EXTERNAL INFORMATION Description Ind1 Ind2 Ind3 Indn SEX AGE . . . Y K K MATRIX CATEGORIES MALE FEMALE . . . Self (n = 1245) Supervisors (n = 1444) Peers (n = 2343) Subordinates (n = 2448) Ind1 Ind2 Indn STRU HHRR POLI SYMB Z K DOUBLE CENTRED STRU HHRR POLI SYMB

18. MATRICES W K Description Male Female . . . 25-34 STRU HHRR POLI SYMB W k Self Supervisors Peers Subordinates STATIS Dual Z k Ind1 Ind2 Ind3 Indn STRU HHRR POLI SYMB Mas Fem . . . Ind1 Ind2 Ind3 Indn 25-34 Where = diag (y 1· ) Y k W k STRU HHRR POLI SYMB Male Female . . . 25-34 Canonical Correspondence Analysis (TER BRAAK, 1986)

19. STATIS DUAL W K Description -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 Male S Fema S 2534 S 3544 S 4554 S 5564 S tecn S lice S maes S prof S g-su S g-me S hi-g S Male U Fema U 2534 U 3544 U 4554 U 5564 U tecn U lice U maes U prof U g-su U g-me U hi-g U Male P Fema P 2534 P 3544 P 4554 P 5564 P tecn P lice P maes P prof P g-su P g-me P hi-g P Male B Fema B 2534 B 3544 B 4554 B 5564 B tecn B lice B maes B prof B g-su B g-me B hi-g B STRU HHRR POLI SYMB Structural Political Symbolic HHRR

20. STATIS DUAL W K Description -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 Political Symbolic Structural HHRR S S S S S S S S S S S U U U U U U U U U P P P P P P P P B B B B B B B S U U U U P P B B B B S P P B B S elf (n = 1245) S U pervisors (n = 1444) P eers (n = 2343) Su B ordinates (n = 2448)

21. STATIS DUAL W K Description -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 Political Symbolic Male _S Fema _S Male _U Fema _U Male _P Fema _P Male _B Fema _B Structural HHRR S elf (n = 1245) S U pervisors (n = 1444) P eers (n = 2343) Su B ordinates (n = 2448) Male Fema le Sexo