Factor analysis means that research is extracted from variable groupsCommon Factor OfStatistical techniques。It was first developed by British psychologist CE. Spearman proposed.He found that there was a certain correlation between students' scores in various subjects. Students who scored well in one subject often scored well in other subjects, so he speculated whether there were some potential common factors, or some general intelligence conditions, that affected students' academic performance.Factor analysis can find hidden representative factors in many variables.By grouping variables of the same nature into a factor, the number of variables can be reduced, and the hypothesis of the relationship between variables can also be tested.
Chinese name
factor analysis
Foreign name
factor analysis
Research
Extracting common factors from variable groups
Proposer
C. E. Spearman
Methods
Center of gravity method, image analysis method, etc
Factor analysis is a statistical method to simplify and analyze high-dimensional data.Assumed p-dimensionRandom vectorsatisfy
Is a q-dimensional random variable,
, satisfied
, its component
It is called the common factorXEach component of plays a role.
Is a p-dimensional unobservable random vector, satisfying
And
,eComponent of
It is called special factor, and it only appliesXComponent of
work.
μ and A are parameter matrices.ifXIf the above formula is satisfied, it is called random vectorXIt has a factor structure.At this time, it is easy to calculate
The influence of is greater than that of special factors
It can also be seen that
Reflects the component
For common factors
The degree of dependence of.
On the other hand, for a specified common factor
，记
, called common factor
yesXContribution of.
The higher the value of, the more common the factor
yesXThe greater the impact of
It is a measure of the importance of common factors.[1]
Recessive variable
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The main purpose of factor analysis is to describe some more basic but not directly measurable latent variables (latent factors) hidden in a group of measured variables. For example, if you want to measure students' enthusiasm for learning, active participation in the classroom, homework completion, and extracurricular reading time, you can use them to reflect enthusiasm.The academic performance can be reflected by the mid-term and final results.Here, learning enthusiasm and academic performance cannot be measured directly by one measure (such as a question). They must be measured by a set of measurement methods, and then the measurement results can be combined to grasp more accurately.In other words, these variables cannot be measured directly.What can be measured directly may be just a representation it reflects, or a part of it.Here, representation and part are two different concepts.Representation is directly determined by this implicit variable.The implicit variable is the cause and the representation is the result. For example, learning enthusiasm is a major determinant of classroom participation (representation measure).
Factor analysis is a powerful tool for social research, but it is not certain that a study contains several factors. When the variables selected in the study change, the number of factors will also change.In addition, the interpretation of the actual meaning of each factor is not absolute.
Get factor
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There are two types of factor analysis methods.One isExploratory factor analysis, the other isConfirmatory factor analysis。Exploratory factor analysis does not assume the relationship between factors and measurement items in advance, but lets the data "speak for themselves".principal component analysisAnd co factor analysis is one of the typical methods.Confirmatory factor analysis assumes that the relationship between factors and measure terms is partially known, that is, which measure term corresponds to which factor, although we do not yet know the specific coefficient.
Validation factor
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The exploratory factor analysis has some limitations.First, it assumes that all factors (after rotation) will affect the measure term.In actual research, we tend to assume that there is no causal relationship between one factor, so it may not affect the measure term of another factor.Second, exploratory factor analysis assumes the measure termresidualThey are independent of each other.In fact, the residuals of measurement terms can be related to single method bias, sub factors and other factors.Third, exploratory factor analysis forces all factors to be independent.Although this is necessary to solve the number of factorsa matter of expediencyHowever, it is inconsistent with most research models.Most obviously, independent variables and dependent variables should be related, rather than independent.These limitations require a more flexible modeling method, so that researchers can not only describe the relationship between measure items and factors in more detail, but also test the relationship directly.In exploratory factor analysis, a tested model (such as orthogonal factors) is often not the exact model in the researchers' theory.
Analysis description
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The strength of confirmatory factor analysis is that it allows researchers to clearly describe atheoretical modelDetails in.So what does a researcher want to describe?We have mentioned that researchers need to use multiple measurement terms because of the existence of measurement errors.When multiple measure terms are used, we have the "quality" problem of measure terms, that is, validity test.The validity test is to see whether a measure item has a significant load with its designed factor, and has no significant load with its unrelated factors.Of course, we may further test whether there is a single method bias in a measure item tool, and whether there are "sub factors" between some measure items.These tests require researchers to clearly describe the measurement items, factorsresidualRelationship between.The description of this relationship is also called measurement model.The quality inspection of the measurement model ishypothesis testThe necessary steps before.
Confirmatory factor analysis often usesmaximum likelihood estimation method Solve.It is often used in conjunction with the structural equation method.For the specific use process and principle, please refer to the Social Survey Research Methods in the expanded reading.
Factor application
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staymarket researchIn, researchers are concerned with the integration or combination of some research indicators, which are usually measured by rating problems, such as usingLikert scaleGets the variable of.The set of each indicator (or a group of associated indicators) is a factor, and the indicator concept grade score is the factor score.
Factor analysis is widely used in market research, mainly including:
(1) Research on Consumer Habits and Attitudes (U&A)
(2) Research on brand image and characteristics
(3) Service quality survey
(4) Personality test
(5) Image survey
(6) Market segmentation identification
(7) Classification of customers, products and behaviors
In practical application, the importance indicators of different factors can be obtained through factor scores, and managers can decide the market problem or product problem to be solved first according to the importance of these indicators.
The task of factor analysis is toXCorrelation matrix and
Depart throughvarianceMaximum orthogonal rotation, calculate the columns of matrix A, and make the corresponding "contributions" in order
