臺灣博碩士論文加值系統

Perturbation theory provides a useful tool for sensitivity analysis in statis-
tical models. In factor analysis influence functions with single-perturbation
have been discussed by Reinhold (2002) who developed the influence function
for factor loading to detect the influential points/outliers. However single-
perturbation diagnostics can suffer from the masking effect, hence in this
thesis we focus on developing the pair-perturbation influence functions to
uncover the masked influential points. Two examples are provided to illus-
trate these approaches.

Contents
Abstract 1
1 Introduction 2
2 Factor Analysis 3
2.1 Factor Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 The Orthogonal Factor Model . . . . . . . . . . . . . . . . . . 3
3 Pair-Perturbations Influence Functions 5
3.1 Influence Function . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Influence Function in FA . . . . . . . . . . . . . . . . . . . . . 6
3.3 Empirical Influence Function . . . . . . . . . . . . . . . . . . . 8
3.4 Deleted Influence Function . . . . . . . . . . . . . . . . . . . . 9
3.5 Sample Influence Function . . . . . . . . . . . . . . . . . . . . 10
3.6 Cut Points Selection of Influential Functions . . . . . . . . . . 11
4 Conclusions 11
Appendix 35

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