《统计与矩阵分析》配套教学课件.pptVIP

* * * * * * * * * * * * * * * * * * * * ORTHOGONAL FACTOR MODEL * ORTHOGONAL FACTOR MODEL * ORTHOGONAL FACTOR MODEL * ORTHOGONAL FACTOR MODEL * 正交变换（因子旋转） * PRINCIPAL COMPONENT SOLUTION * PRINCIPAL COMPONENT SOLUTION * RESIDUAL MATRIX * DETERMINATION OF NUMBER OF COMMON FACTORS * EXAMINATION SCORES（因子旋转） * MAXIMUM LIKELIHOOD SOLUTION * FACTOR ROTATION * ROTATED FACTOR LOADING * 对应分析 * 列联表 * * * * * * * * * * * * * * * * PRINCIPAL COMPONENT ANALYSIS Explain the variance-covariance structure of a set of variables through a few linear combinations of these variables Objectives Data reduction Interpretation Does not need normality assumption in general * PRINCIPAL COMPONENTS * RESULT （主成分解） * RESULT （总方差不变） * PROPORTION OF TOTAL VARIANCE DUE TO THE KTH PRINCIPAL COMPONENT * CONCEPT OF PRINCIPAL COMPONENTS * SAMPLE PRINCIPAL COMPONENTS * SAMPLE PRINCIPAL COMPONENTS * EXAMPLE : PAINED TURTLES * EXAMPLE * EXAMPLE : TURTLE DATA * EXAMPLE : SCREE PLOT * EXAMPLE * 几何解释 * 几何解释 * 几何解释 * 几何解释 * 几何解释 * 几何解释 * 几何解释 * 几何解释 * 样本主成分 * EXAMPLE: PAINED TURTLES * EXAMPLE * EXAMPLE: SCREE PLOT * EXAMPLE * 样本主成分的近似平面解释 * * 因子分析 * HISTORY Early 20th-century attempt to define and measure intelligence Developed primarily by scientists interested in psychometrics Advent of computers generated a renewed interest Each application must be examined on its own merits * ESSENCE OF FACTOR ANALYSIS Describe the covariance among many variables in terms of a few underlying, but unobservable, random factors. A group of variables highly correlated among themselves, but having relatively small correlations with variables in different groups represent a single underlying factor * EXAMINATION SCORES * ORTHOGONAL FACTOR MODEL SAMPLE MEAN AND SAMPLE VARIANCE * SAMPLE COVARIANCE AND SAMPLE CORRELATION COEFFICIENT * STANDARDIZED VALUES (OR STANDARDIZED SCORES) Centered at zero Unit standard deviation Sample correlation coefficient can be regarded as a sample covariance of two standardized variables *