Abstract

Multivariate analysis refers to statistical techniques that simultaneously look at three or more variables in relation to the subjects under investigation with the aim of identifying or clarifying the relationships between them.

These techniques have been broadly classified as dependence techniques, which explore the relationship between one or more dependent variables and their independent predictors, and interdependence techniques, that make no such distinction but treat all variables equally in a search for underlying relationships.

Multiple linear regression models a situation where a single numerical dependent variable is to be predicted from multiple numerical independent variables. Logistic regression is used when the outcome variable is dichotomous in nature.

The log-linear technique models count type of data and can be used to analyze cross-tabulations where more than two variables are included. Analysis of covariance is an extension of analysis of variance (ANOVA), in which an additional independent variable of interest, the covariate, is brought into the analysis.

It tries to examine whether a difference persists after “controlling” for the effect of the covariate that can impact the numerical dependent variable of interest. Multivariate analysis of variance (MANOVA) is a multivariate extension of ANOVA used when multiple numerical dependent variables have to be incorporated in the analysis.

Interdependence techniques are more commonly applied to psychometrics, social sciences and market research. Exploratory factor analysis and principal component analysis are related techniques that seek to extract from a larger number of metric variables, a smaller number of composite factors or components, which are linearly related to the original variables.

Cluster analysis aims to identify, in a large number of cases, relatively homogeneous groups called clusters, without prior information about the groups.

The calculation intensive nature of multivariate analysis has so far precluded most researchers from using these techniques routinely.

The situation is now changing with wider availability, and increasing sophistication of statistical software and researchers should no longer shy away from exploring the applications of multivariate methods to real-life data sets.

2024/0829
1.基本介紹 C1-4
2.多變量統計方法介紹 C5-10
Logit & Probit回歸、主成份分析、因素分析、區別分析、典型相關分析、集群分析 等6個章節
請簡要介紹有關多變量統計方法的以下六個方法：Logit & Probit回歸、主成份分析、因素分析、區別分析、典型相關分析、集群分析
信度與效度分析 C11-12
3.統計軟體使用 C11-
4.相關及變異數分析、迴歸分析

本書是以多變量統計方法在管理上的應用為主軸，因此在例題的選取上，包括
1.個別管理功能所需分析的問題，市場資料及企業內部生產資料
2.整體企業的財務資料及產業資料分析
3.總體經濟資料及國家競爭力資料分析

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Ch1習題： 2024/08/29
1.變數衡量的尺度有哪四類?各種尺度的變數有什麼不同?分別舉三個例子來說明 這是變數類型的分類
nominal scale, ordinal scale, interval scale, ratio scale
名目 (分類:男女,有無，ABC..類) 性別、教育、職業、產業..; 無關大小、沒有次序、(即有編號)不可運算。
序列 可排序先後、強弱、等級(如Likert scale); 次序有意義、數字無等距、不可運算。
區間 可排序、數距有意義，可加減運算，有任意原點、無絕對原點、乘除和比率無意義(不可說10度C比5度C熱兩倍)
比率 有絕對原點，可四則運算，如身高、體重、GDP、營業額

2.請解釋什麼是依賴模式dependence？ 相依模式interdependence？ 及結構關係模式strucrural？ 這是統計方法的三種分類
1)依賴模式dependence或稱因果關係couse-and-effect模式: 可以在一堆變數中，分辨出那些是因變數(解釋變數)？ 那些是依變數(反應變數)？ 但不必然有因果關係。
2)相依模式interdependence： 當無法分辨變數或資料的依賴關係時，用相依模式找出其如何how與為什麼Why相關的。但無法看出那些變數受那些變數影響。
3)strucrural結構模式是描述一群可觀測或不可觀測變數間的結構及系統關係，(這是第二代多變量統計方法)。
3.依賴模式的統計分析方法可依那些標準來分類？各種分類之下有哪些統計方法？

Subhash Sharma Applied Multivariate Techniques -Table

4.相應模式和依賴模式有什麼共同點?有什麼差異? 5.為什麼時間序列資料比較不適合被用來進行多變量分析?