Method function
applied range
Application mode
application program
evaluate
Matters needing attention
catalogue
1 summary
2 Basic information
3 method function
4 Scope of application
factor
economy
5 method of use
Continuous substitution
variation analysis
Exponential decomposition
Fixed base substitution
6 application program
General procedure
Principle of use
7 evaluation
Eight preventive measures
9 references
Factor analysis. Also known as empirical analysis, it is a qualitative analysis method. This method mainly refers to determining the selected object through collective research on the basis of various factors that should be considered in the selection of value engineering objects and the knowledge and experience of analysts. This method is simple, requires value engineers to be familiar with products and have rich experience, and is suitable for situations where the research objects are quite different or the time is short. The disadvantage is that there is no quantitative analysis and the subjective influence is great.
Factor analysis is a statistical analysis method to analyze the influence degree of each factor in the total change of phenomenon by using statistical index system, including sequence substitution method, difference analysis method and index decomposition method. Factor analysis is an important and practical method in modern statistics and a branch of multivariate statistical analysis. Using this method, researchers can simplify a set of variables that reflect the nature, state and characteristics of things into a few factors that can reflect the internal relations of things and determine the essential characteristics of things.
Basic information
Chinese name
Factor analysis method
Another name
Exponential factor analysis
classify
Series substitution method, difference analysis method, etc.
Method function
The biggest function of factor analysis is to deal with the external characteristics and relationships of observable things from the outside to the inside, from here to there, from coarse to fine, from false to true by mathematical methods, so as to summarize the universal nature of objective things. Secondly, the use of factor analysis can greatly simplify complex research topics and maintain their basic information.
applied range
factor
By analyzing the supply and demand situation of futures commodities and its influencing factors, the changing trend of futures prices is explained and predicted. Futures trading is based on spot trading. There is a close relationship between futures price and spot price. The supply and demand of commodities and many factors affecting their supply and demand have an important impact on the commodity price in the spot market, and therefore will inevitably have an important impact on the futures price. Therefore, by analyzing the changes of commodity supply and demand and its influencing factors, it can help futures traders predict and grasp the basic trend of commodity futures price changes. In the real market, futures prices are not only affected by the relationship between supply and demand of commodities, but also by many other non-supply and demand factors. These non-supply and demand factors include: financial and monetary factors, political factors, policy factors, speculative factors, psychological expectations and so on. Therefore, the analysis of the basic factors of futures price trend needs to comprehensively consider the influence of these factors. [ 1]
economy
The supply and demand of commodities have an important influence on commodity futures prices. Basic factor analysis mainly analyzes the relationship between supply and demand. The change of commodity supply and demand and the change of price influence and restrict each other. Commodity prices are inversely proportional to supply, supply increases and prices fall; Supply decreases and prices rise. Commodity prices are directly proportional to demand, demand increases and prices rise; Demand decreases and prices fall. With other factors unchanged, any change in the relationship between supply and demand may affect the change of commodity prices. On the one hand, the change of commodity prices is influenced by the change of supply and demand; On the other hand, changes in commodity prices have an impact on supply and demand in turn: prices rise, supply increases, and demand decreases; As prices fall, supply decreases and demand increases. This interaction and causal relationship between supply and demand and price makes the analysis of commodity supply and demand more complicated, that is, not only the influence of supply and demand changes on prices, but also the reaction of price changes on supply and demand should be considered.
Application mode
Continuous substitution
It decomposes the analysis index into measurable factors, and replaces the reference value (usually the standard value or the planned value) with the comparison value (usually the actual value) of each factor in turn according to the dependency relationship between each factor, so as to measure the influence of each factor on the analysis index.
For example, assuming that the analysis indicator M is obtained by multiplying three interrelated factors A, B and C, the reporting period (actual) indicator and base period (planned) indicator are:
The (actual) indicator in the reporting period is m1= a1* b1* c1.
Base period (plan) indicator M0=A0 * B0 * C0
When determining the influence degree of the change index of each factor on the index r, it can be carried out in turn:
Base period (plan) indicator M0 = A0 * B0 * C0...( 1)
Replace A1* B0 * C0 for the first time ... (2)
Replace a1* b1* c0 for the second time ... (3)
The third substitution of A 1 * B 1 * C 1 ... (4)
The analysis is as follows:
(2) The influence of the change of-(1) → A on M.
(3)-(2) → The influence of B change on M.
(4)-(3) → The influence of the change of C on M.
The total impact is △ m = m1-m0 = (4)-(3)+(3)-(2)+(2)-(1).
variation analysis
It is a simplified form of serial substitution method, which uses the difference between the comparison value of each factor and the reference value to calculate the influence of each factor on the analysis index.
For example, the relationship between a financial indicator and related factors consists of the following formulas: actual indicator: Po = Ao× Bo× Co standard index: PS = as× bs× cs. The total difference between actual and standard is po-PS, which is influenced by three factors: A, B and C, and their respective influence degrees can be calculated by the following formulas:
The influence of a factor change: (ao-as) × bs× cs;
The influence of the change of factor B; ao×(Bo-Bs)×Cs；
The influence of the change of factor c: Ao×Bo×(Co-Cs).
Finally, the sum of the respective influence numbers of the above three factors should be equal to the total difference Po-Ps.
Exponential decomposition
For example, the profit rate of assets can be decomposed into the product of asset turnover rate and sales profit rate.
Fixed base substitution
Replace the standard value with the analysis value respectively, and determine the influence of various factors on financial indicators, such as the difference analysis of standard cost.
application program
General procedure
1, to determine the indicators to be analyzed;
2. Determine the factors affecting the index and their relationship with the index;
3. Calculate and determine the influence degree and quantity of each factor.
Principle of use
People's psychological phenomenon is complex, which is formed by the organic combination of various factors, and each psychological factor is restricted by various conditions at the same time. It is like a huge multidimensional system, which regulates people's behavior. Traditional univariate and bivariate analysis often lose useful information or introduce useless information in information processing, which makes researchers unable to distinguish between primary and secondary phenomena or draw inappropriate or even wrong conclusions. Factor analysis can comprehensively reflect different aspects of things on the basis of multivariate observation and analysis. In psychological research, researchers use factor analysis to extract several decisive factors from many variables, establish theoretical assumptions, and then use factor analysis to repeatedly verify the assumptions until they succeed. Therefore, factor analysis is a powerful cognitive means and auxiliary tool to form scientific concepts and then build ideological models and theoretical systems.
The mathematical operation of factor analysis is mainly based on matrix operation. The basic operation process is as follows:
The first is to collect certain measurement data and standardize the data. In psychological measurement, it is often necessary to convert test scores into standard scores and organize them into a data matrix.
Secondly, the correlation matrix of each factor and other factors is obtained through correlation operation.
Thirdly, the factor load matrix is obtained by using specific operation methods, such as principal component analysis, image analysis, α factor analysis, minimum residual factor analysis, maximum possible solution, gravity center method and so on.
Fourthly, in order to make the meaning of the load matrix clear and easy to analyze, the right-angle rotation method and the oblique rotation method should be used to deal with the load matrix, so that each variable only has a large load on a few factors, and the load of some variables is close to zero. This may make the factors of each variable more concentrated in the total variance, thus showing the most meaningful characteristic principal factor among the variables.
Fifth, define and explain the main factors. Whether the definition of principal factor is accurate and the explanation is appropriate depends not only on the success of factor analysis, but also on the subjective judgment process to a great extent. This is especially true when the results of factor analysis are not clear.
Application of Factor Analysis in Intelligence Test
The application of factor analysis begins with the study of intelligence. 1904, Spearman published the article "Objectively Measuring Intelligence", which initiated the study of intelligence by factor analysis. In the process of analyzing students' test scores, Spearman noticed that the correlation matrix between scores has a certain systematic influence. Its correlation matrix is as follows:? The courses in the table are arranged in descending order from left to right according to the correlation coefficient, and the values in each row are generally reduced to the same degree. Spearman pointed out through analysis that the test scores of each course can be regarded as the sum of a general factor (consistent with general intelligence) and a special factor (consistent with special intelligence). He made repeated calculations on various experiments, and most of them got similar results. Therefore, he thinks that any intelligence factor is composed of general factor G and special factor S, which is the famous two-factor theory of intelligence.
Since then, thurston and others have extracted more than 60 factors through factor analysis of more than 60 different types of intelligence tests, and found seven stable factors: calculation, word fluency, verbal meaning, memory, reasoning, spatial perception and perceptual speed, which are called "basic psychological ability", which is thurston's theory of intelligence group factors. Thurston and his colleagues tested every stable ability factor and predicted that these abilities should be negatively correlated. However, each ability is positively correlated with other abilities. It seems that there are still general factors in various abilities. They compiled the PMAT test and analyzed the data of the PMAT test, and found that there are still two groups of factors, namely, language education ability, space mechanical ability and practical activity ability. Vernon in 1950 made various factors form different levels of branches through factor analysis. The highest is the general factor G, followed by the ability of language education, space machinery and practical activities, then the smaller PMAT subgroup factor, and finally the special factor S. Through the factor analysis of the measurement results, they divide the intelligence into hierarchical structures.
Guildford's theory of intellectual structure also benefits from factor analysis. He put forward a three-dimensional model of intelligence structure, thinking that intelligence consists of three variables: operation, content and result, which include five, four and six aspects respectively, and intelligence factor *** 120. Later, he increased the intelligence factor of 120 to 150. In order to prove the existence of this 150 intelligence factor, he designed an intelligence test and verified it with factor analysis. He claimed that he had found more than 100 intelligence factors, and it was almost impossible to extract so many independent variables without factor analysis.
Cattel and Horn put forward their own theory of intelligence structure by analyzing the factors of test, and thought that the general intelligence factors were fluid intelligence GF and crystal intelligence GC. GF loads numerical ability, spatial ability and reasoning ability, while GC loads language ability, reasoning ability, memory ability and word fluency. His theory supports Spearman's theory of two factors of intelligence.
The theoretical basis of wexler's intelligence test comes directly from Spearman's intelligence two-factor theory and thurston's group factor theory. Webster believes that people's general intelligence is the synthesis of various abilities, so his intelligence test benefits from factor analysis. Cohen made a factor analysis of W-B, WAIS and WISC, the predecessors of Wechsler Adult Intelligence Scale, and found that Wechsler Adult Intelligence Scale contains five identical factors: speech comprehension I, perceptual organization, memory or concentration, and speech.