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Factor Analysis Statistical Method Assignment Help, Types of Factor Analysis
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>> Fa >> Factor Analysis Statistical Method Assignment Help, Types of Factor Analysis
因素分析 - 统计方法
因子分析是,用于描述各种观察到的变量之间有效性的统计方法,这些变量也被称为因素。因子分析是为了寻找响应未观察到的潜在变量的关节变化。然后将观察到的变量建模为所有潜在因素的线性组合以及误差项。与观察到的变量相互依存有关的信息用于减少数据集中的变量集。当我们有一组P随机可观察变量时,其中x
1
, ....X
p
和手段
1
,....,你
p
,
We get
e
i
is independently distributed items of error having zero mean and a finite variance, which might not be same for all the i’s.
For n observations, the dimensions will be x
p*n
, L
p*k
, F
k*n
Here the value of a particular observation is denoted by x and F. The matrix L does not vary across observations.
We can assume the assumptions on F
1. f and e are independent
2. E(F)=0
3. Cov(F)=1
具有F的约束的上述方程组的解决方案被拒绝,因为这些因素和L称为加载矩阵。
Assuming Cov (x − μ) = Σ, then form the conditions just imposed on F we get,
For any orthogonal matrix Q , if we set L=LQ and F=Q
T
f,是因素F的标准,是因素和因子持有的标准,因此,仅与正交转换的因素和因子保持相同。
Type of factor analysis
1. Exploratory data analysis or EFA- is used for covering underlying structure of a relatively larger set of variables. The a priori assumption is that any indicator might be indicated with any factor. This can be termed as the most common form of factor analysis found. Factor loadings are used for intuiting the factor structure of the data and there is no prior theory. ctor analysis or2. Confirmatory factor analysis or CFA is used for determining whether the number of factors as well as the loadings of indicator variables lying on them confirm to what is expected in real on the axis of a pre established theory. The selection of independent variables is done on the basis of prior theory and we use the factor analysis to see whether they as per the predicted manner on expected number of all factors.
Types of factoring
1. The principal component analysis- it can be termed as the most common form of factor analysis which seeks linear combination of variables such that we can extract the maximum variances from the variables. r analysis- it is also known as the Rao’s canonical factor analysis, which is entirely a different method of computing and seeks factors that have the highest canonical correlation with the observed variables.
3. The common factor analysis-. The other names of common factor analysis are the principal factor analysis and the principal axis factoring. It seeks the least number of factors which account for some common variances of the set of variable.
4.图像分解 - 这是基于预测变量而不是实际变量的相关矩阵,并且通过使用多重回归从其他变量预测每个样本。
5. alpha保理 - 这是基于因素的可靠性,假设变量是从变量宇宙中随机采样的。这使其与假定要固定的情况样本和变量的其他方法不同。
6. Factor regression model- this is a ki6. Factor regression model- this is a kind of combinational mole obtained form combining regression model and factor model. It can also be termed as a hybrid model whose factors are only partially known.
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