Factor analysis in economics. On the topic “Methodology of factor analysis

3. When using the method of absolute differences, the magnitude of the influence of factors is calculated by multiplying the absolute increase in the factor under study by the base value of the factors that are to the right of it and by the actual value of the factors located to the left of it in the model. The calculation is based on the sequential replacement of the planned values ​​of factor indicators with their deviation, and then with the actual level of these indicators.

4. Let a factor multiplicative model be given and the values ​​of the indicators in the base y0, a0, b0, c0 and reporting periods y1, a1, b1, c1 are known. Let us determine the influence of each factor on the effective indicator “y”.

5. -- influence of factor “a”
-- influence of factor "b"
-- influence of factor “c”

Stages of the emergence and development of economic analysis

1.Middle 19th century. centuries, the emergence of economic analysis. The emergence of economic analysis is associated with the practical need to verify the solvency of the buyer of goods to whom the seller provides payment in installments. Consequently, the earliest type of economic analysis is financial analysis. At this time, the formation and development of balance sheet science (accounting) took place and within its framework the first simple methods of analytical research appeared.

2.Second half of the 19th century.– highlighting theoretical and practical economic analysis in the era of development of capitalist relations

3. First half of the 20th century.– isolation of microeconomic analysis, i.e. analysis of economic activities of enterprises. In addition, in the 30s of the 20th century. The analysis of the economic activities of enterprises as a science is becoming established, at this time ACD is being introduced into the programs of universities of the USSR.

4. Second half of the 20th century.– at this time, a thorough development of independent areas of analysis methodology takes place (there are such methods as: functional-cost, economic-mathematical, etc.)

5. Current state of analysis is a science thoroughly developed in theoretical and practical terms, which involves the widespread use of mathematical methods and computers.

4. Factor analysis of profit (loss)

Factor analysis of profit

Identification of causes and their impact on profit indicators is most appropriately carried out using factor analysis. Let's consider the analysis methodology using an additive type model to analyze sales profit.

The essence of factor analysis is to identify how much each of the following factors influenced the change in profit in rubles:

1. sales revenue
2. price
3. cost
4. Selling and administrative expenses
5. How, in general, did all these factors affect sales profit?

Moreover, the combined influence of all factors must correspond to the absolute deviation (column 5) of profit from sales in the reporting year compared to the base year.

This analysis is carried out in several stages:

1. calculation of the influence of the “sales revenue” factor: such an analysis begins with taking into account the influence of inflation. The explanatory note in the accounting report usually contains information about how much the prices for the company's products have increased on average over the year. Knowing this%, they calculate sales revenue in the reporting period in comparable prices with the base period. Without achieving such a comparison, analysis is meaningless.

Vsop. report = In report /I c
Vsop. otch - revenue of the reporting period in comparable prices (prices of last year);
In the report - the revenue of the reporting period, given in Form No. 2 at the prices of the reporting period;
I c - price index (inflation index);
It follows from this: revenue from product sales in the reporting year increased due to price increases as follows:

Vc=Watch.–Additional report.
Vts – change in sales revenue due to price (inflation)

The effect on the amount of profit from sales (Pp) of changes in sales revenue, excluding the effect of changes in price, can be calculated as follows:

Ppz - (Watch - Vbalance) -Vts)/100 * P p basis
P p = Pp / Revenue
Рп – profitability from sales.

2. Calculation of the influence of the factor “cost of sales” (production cost) (line 020 of Form No. 2). This influence is calculated using the formula:

Pps=Watch. * (Us0 - Usb)/100
U s0 and U sb – the share of the cost of revenue in the reporting and base years, %.

This information is taken from the calculation tables (see question 1) - columns 6 and 7.

3. Calculation of the influence of the “price” factor

P pc = Vc *P p basis /100

4. Calculation of the “commercial expenses” factor

P cr = In report * (U cr report -U cr. base)/100
At the cr.otch. and bases – columns 6 and 7.

5. Calculation of the “administrative expenses” factor

Pupr. =Watch. *(Uuro -U urb)/100
Where Uuro and U ur are, respectively, the levels of management expenses in the reporting and base periods

6. Calculation of the total influence of all factors on sales profit

The “Total” amount must be equal to the absolute deviation on line 050 of Form No. 2 (column 5). If this is not the case, then the calculations are erroneous and further analysis makes no sense.

Factor analysis can be continued to net income. The methodology for carrying it out is as follows:

1. According to the above diagram, sales profit is analyzed.
2. The influence of all other factors (operating income, expenses, etc.) is assessed in column 5 in the table above.

5. The place of economic analysis in the system of economic sciences

The economic side of economic activity is the object of all economic sciences. But each economic science has its own subject of study, i.e. explores some feature, side or form of movement of this general object.

-Classifying economic sciences according to the subject of research, the following groups can be distinguished:

1. General theoretical, fundamental– economic theory, history of economic doctrines; the subject of the study is economic relations and productive forces in the aggregate.

2. Industry– industry, construction, agriculture, etc.; The subject of the study is economic relations and productive forces in the context of individual industries.

3. Territorial (regional) – world economy and international economic relations, the economy of developed capitalist countries, the economy of socialist countries, the economy of developing countries, etc.; The subject of the study is economic relations and productive forces by region.

4. Special – finance, money circulation, credit, labor economics, etc.; the subject of research is a certain set of homogeneous relations and related productive forces.

5. Managerial functional – accounting, statistics, economic analysis, planning, operational management, control; the subject of research is a certain basic management function (each of the sciences has its own management function).

Thus economic analysis is an independent science belonging to the management group of economic sciences.

6.Factor analysis of income

The relevance of the issues of factor analysis of income, the efficiency of managing assets that generate future income, and the use of systems for early identification and prevention of structural risks that arise in the process of planning and budget execution and are significant from an economic point of view, has increased significantly over the past few years.

The current economic situation is promoting increased interest in high-performance solutions for automating the processes of risk analysis, control and monitoring in real time. The need for advanced forecasting functions becomes a priority, and the task of identifying factor dependencies in the process of income analysis becomes of paramount importance to ensure the timeliness and validity of management decisions.
Today, most software manufacturing companies have a fairly wide product line that allows them to provide an integrated approach to automating analysis functions. The use of such software as a tool for effective revenue management allows you to implement the required risk management methodology and at the same time helps to increase the degree and completeness of coverage of the analyzed information and ensures the effectiveness of the subsequent use of the analysis results.

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Identification of the relationship between performance indicators and factor indicators, the form of dependence between them. Features of the application of the elimination method, integral and index methods. Mathematical methods of factor analysis.

Factors are the conditions of economic processes and the reasons influencing them.

Factor analysis is a technique for comprehensive systemic study and measurement of the impact of factors on the value of an effective indicator.

All phenomena and processes of economic activity of enterprises are in relationships, interdependence and interdependence. One of them directly are interconnected, others - indirectly . For example, the amount of profit from the core activities of an enterprise is directly influenced by such factors as the volume and structure of sales, selling prices and production costs. All other factors influence this indicator indirectly. Each phenomenon can be considered both as a cause and as a result. For example, labor productivity can be considered, on the one hand, as the reason for changes in the volume of production, the level of its cost, and on the other hand, as a result of changes in the degree of mechanization and automation of production, improvement in labor organization, etc. If this or that indicator is considered as a consequence, as a result of the action of one or more causes and acts as an object of study, then when studying relationships it is called an effective indicator. Indicators that determine the behavior of an effective characteristic are called factor indicators.

Each performance indicator depends on numerous and varied factors. The more detailed the influence of factors on the value of the performance indicator is studied, the more accurate the results of the analysis and assessment of the quality of work of enterprises. Hence, an important methodological issue in the analysis of economic activity is the study and measurement of the influence of factors on the value of the economic indicators under study. Without a deep and comprehensive study of factors, it is impossible to draw reasonable conclusions about the results of activities, identify production reserves, justify plans and management decisions, predict performance results, and assess their sensitivity to changes in internal and external factors.

Under factor analysis understand the methodology for comprehensive and systematic study and measurement of the impact of factors on the value of performance indicators.

The following are distinguished: types of factor analysis:

Deterministic (functional) and stochastic (probabilistic);

Direct (deductive) and reverse (inductive);

Single-stage and multi-stage;

Static and dynamic;

Retrospective and prospective (forecast).

Based on the nature of the relationship between indicators, methods of deterministic and stochastic factor analysis are distinguished.

Deterministic factor analysis is a technique for studying the influence of factors whose connection with the performance indicator is functional in nature, i.e. the effective indicator can be presented as a product, quotient or algebraic sum of factors.

Stochastic factor analysis explores the influence of factors whose connection with the performance indicator, in contrast to the functional indicator, is incomplete, probabilistic (correlation). If with a functional (complete) dependence with a change in the argument there is always a corresponding change in the function, then with a stochastic connection a change in the argument can give several values ​​of the increase in the function depending on the combination of other factors that determine this indicator. For example, labor productivity at the same level of capital-labor ratio may be different at different enterprises. This depends on the optimal combination of all the factors that form this indicator.

With direct factor analysis The research is conducted in a deductive manner - from the general to the specific. Back factor analysis carries out the study of cause-and-effect relationships using the method of logical induction - from particular, individual factors to general ones. It allows you to assess the degree of sensitivity of performance results to changes in the factor under study.

Factor analysis can be single-stage or multi-stage. Single stage used to study factors of only one level (one level) of subordination without detailing them into their component parts. For example, y = a b. With multi-stage factor analysis Factors a and b are detailed into their constituent elements in order to study their essence. The factors can be further detailed. In this case, the influence of factors at different levels of subordination is studied.

It is also necessary to distinguish between static and dynamic factor analysis . The first type is used when studying the influence of factors on performance indicators on the corresponding date. Another type is a technique for studying cause-and-effect relationships in dynamics.

Finally, factor analysis can be retrospective , which studies the reasons for changes in the results of economic activities over past periods, and prospective , which examines the behavior of factors and performance indicators in perspective.

Main tasks of factor analysis

1. Selection of factors for the analysis of the studied indicators.

2. Classification and systematization of them in order to provide a systematic approach.

3. Modeling the relationships between performance and factor indicators.

4. Calculation of the influence of factors and assessment of the role of each of them in changing the value of the effective indicator.

5. Working with the factor model (its practical use for managing economic processes).

To study the influence of factors on business results and calculate reserves, the analysis uses methods of deterministic and stochastic factor analysis, methods for optimizing solutions to economic problems(see picture).

Determining the magnitude of the influence of individual factors on the increase in performance indicators is one of the most important methodological tasks in ACD. In deterministic analysis, the following methods are used for this: chain substitution, absolute differences, relative differences, index, integral, proportional division, logarithm, balance, etc.

The main properties of the deterministic approach to analysis:

Construction of a deterministic model through logical analysis;

The presence of a complete (hard) connection between indicators;

The impossibility of separating the results of the influence of simultaneously acting factors that cannot be combined in one model;

Studying relationships in the short term.

Let's consider the possibility of using the main methods of deterministic analysis, summarizing the above in the form of a matrix

Matrix of application of deterministic factor analysis methods

Legend: + used;

- not used

There are four types of deterministic models:

Additive models represent an algebraic sum of indicators and have the form:

Such models, for example, include cost indicators in relation to elements of production costs and cost items; an indicator of the volume of production of goods in its relationship with the volume of output of individual products or the volume of output in individual departments.

Multiplicative is the sequential division of the factors of the original system into factor factors. Models in a generalized form can be represented by the formula:

An example of a multiplicative model is a two-factor model of gross output: VP = CR * SV

where CR is the average number of employees;

CB - average annual output per employee.

Multiple models: y = x1 / x2.

An example of a multiple model is the indicator of the turnover period of goods (TOB.T) (in days): TOB.T = 3T / OR, (1.9)

where ST is the average stock of goods;

OP - one-day sales volume.

Mixed models are a combination of the above models and can be described using special expressions:

Examples of such models are cost indicators per 1 ruble. manufactured products, profitability indicators, etc.

1. The most universal of the methods of deterministic analysis is the method of chain substitution.

It is used to calculate the influence of factors in all types of deterministic factor models: additive, multiplicative, multiple and mixed (combined). This method is based on elimination.

Elimination is the process of gradually eliminating the impact of all factors on the value of the performance indicator, except one. Moreover, based on the fact that all factors change independently of each other, i.e. First, one factor changes, and all the others remain unchanged. Then two change while the others remain unchanged, etc.

This method allows you to determine the influence of individual factors on changes in the value of the effective indicator. The essence of this technique is to identify from all the existing factors the main ones that have a decisive influence on the change in the indicator. For this purpose, a number of conditional values ​​of the performance indicator are determined, which take into account changes in one, then two, three and subsequent factors, assuming that the rest do not change. This means that in the calculations, private planned indicators are successively replaced with reporting ones, and the results obtained are compared with the available previous data. Comparing the values ​​of a performance indicator before and after changing the level of one or another factor makes it possible to eliminate the influence of all factors except one and determine the impact of the latter on the growth of the performance indicator.

When using the chain substitution method, the sequence of substitutions is of great importance: First of all, it is necessary to take into account changes in quantitative and then qualitative indicators. Using the reverse sequence of calculations does not provide a correct characterization of the influence of factors.

Thus, the use of the chain substitution method requires knowledge of the relationship of factors, their subordination, and the ability to correctly classify and systematize them.

In general, the application of the chain production method can be described as follows:

y0 = a0 ∙ b0 ∙ c0 ;

ya = a1 ∙ b0 ∙ c0 ;

yb = a1 ∙ b1 ∙ c0 ;

y1 = a1 ∙ b1 ∙ c1 ;

where a0, b0, c0 - basic values ​​of factors influencing the general indicator y;

a1, b1, c1 - actual values ​​of factors;

ya, yb, - intermediate values ​​of the resulting indicator associated with changes in factors A And b, respectively.

The total change Δу = у1 – у0 consists of the sum of changes in the resulting indicator due to changes in each factor with fixed values ​​of the remaining factors. Those. the sum of the influence of individual factors should equal the overall increase in the performance indicator.

∆y = ∆ya + ∆yb + ∆yc = y1– y0

∆ya = ya – y0 ;

∆yb = yb – ya ;

∆yc = y1 – yb.

The advantages of this method: versatility of application, ease of calculations.

The disadvantage of the method is that, depending on the chosen order of factor replacement, the results of factor decomposition have different meanings.

2. The method of absolute differences is a modification of the method of chain substitution.

The method of absolute differences is used to calculate the influence of factors on the growth of a performance indicator in deterministic analysis, but only in multiplicative models (Y = x1 ∙ x2 ∙ x3 ∙∙∙∙∙ xn) and models of multiplicative-additive type: Y = (a - b) ∙c and Y = a∙(b - c). And although its use is limited, due to its simplicity it is widely used in ACD.

The essence of the method is that the magnitude of the influence of factors is calculated by multiplying the absolute increase in the value of the factor under study by the base (planned) value of the factors that are to the right of it, and by the actual value of the factors located in the model to the left of it.

y0 = a0 ∙ b0 ∙ c0

∆ya = ∆a ∙ b0 ∙ c0

∆yb = a1 ∙ ∆b ∙ c0

∆yс = a1 ∙ b1 ∙ ∆с

y1 = a1 ∙ b1 ∙ c1

The algebraic sum of the increase in the effective indicator due to individual factors should be equal to its total change Δу = у1 – у0.

∆y = ∆ya + ∆yb + ∆yc = y1 – y0

Let's consider an algorithm for calculating factors using this method in multiplicative-additive models. For example, let’s take the factor model of profit from product sales:

P = VRP ∙ (C - C),

where P is profit from sales of products;

VRP – volume of product sales;

P is the price of a unit of production;

C is the cost per unit of production.

Increase in profit due to changes:

volume of product sales ∆ПВРП = ∆VРП ∙ (Ц0 − С0);

sales yen ∆ПЦ = VРП1 ∙ ∆Ц;

production cost ∆PS = VРП1 ∙ (−∆С);

3. Method of relative differences It is used in cases where the source data contains previously determined relative deviations of factor indicators in percentages. It is used to measure the influence of factors on the growth of a performance indicator only in multiplicative models. Here, relative increases in factor indicators are used, expressed as coefficients or percentages. Let us consider the methodology for calculating the influence of factors in this way for multiplicative models of the type Y = abc.

The change in the performance indicator is determined as follows:

According to this algorithm, to calculate the influence of the first factor, it is necessary to multiply the base value of the effective indicator by the relative increase of the first factor, expressed as a decimal fraction.

To calculate the influence of the second factor, you need to add the change due to the first factor to the base value of the effective indicator and then multiply the resulting amount by the relative increase in the second factor.

The influence of the third factor is determined in a similar way: to the base value of the effective indicator it is necessary to add its increase due to the first and second factors and multiply the resulting amount by the relative increase of the third factor, etc.

The calculation results are the same as when using the previous methods.

The method of relative differences is convenient to use in cases where it is necessary to calculate the influence of a large set of factors (8-10 or more). Unlike previous methods, the number of computational procedures is significantly reduced here, which determines its advantage.

4. The integral method for assessing factor influences avoids the disadvantages inherent in the chain substitution method and does not require the use of techniques for distributing the indecomposable remainder among factors, because it has a logarithmic law of redistribution of factor loads. The integral method makes it possible to achieve a complete decomposition of the effective indicator into factors and is universal in nature, i.e. applicable to multiplicative, multiple and mixed models. The operation of calculating a definite integral is carried out using the computing capabilities of personal computers and comes down to constructing integrand expressions that depend on the type of function or model of the factor system.

Its use makes it possible to obtain more accurate results for calculating the influence of factors compared to the methods of chain substitution, absolute and relative differences, since the additional increase in the effective indicator from the interaction of factors is not added to the last factor, but is divided equally between them.

Let's consider algorithms for calculating the influence of factors for different models:

1) Model view: y = a ∙ b

2) Model view: y = a ∙ b ∙ c

3) View model:

3) View model:

If the denominator has more than two factors, the procedure continues.

Thus, the use of the integral method does not require knowledge of the entire integration process. It is enough to substitute the necessary numerical data into these ready-made working formulas and make not very complex calculations using a calculator or other computer equipment.

The results of calculations using the integral method differ significantly from those obtained by the method of chain substitutions or modifications of the latter. The greater the magnitude of changes in factors, the more significant the difference.

5. The index method allows us to identify the influence of various factors on the studied aggregate indicator. By calculating indices and constructing a time series characterizing, for example, production output in value terms, one can make a qualified judgment about the dynamics of production volume.

It is based on relative indicators of dynamics, expressing the ratio of the level of the analyzed indicator in the reporting period to its level in the base period. Using the index method you can

Any index is calculated by comparing the measured (reported) value with the base one. For example, production volume index: Ivп = VВП1 / VВП0

Indices expressing the ratio of directly comparable quantities are called individual , and the characterizing relationships of complex phenomena are group , or total . Statistics name several forms indices that are used in analytical work - aggregate, arithmetic, harmonic, etc.

By using the aggregate form of the index and following the established computational procedure, it is possible to solve a classic analytical problem: determining the influence of the quantity factor and the price factor on the volume of produced or sold products. The calculation scheme will be as follows:

It should be recalled here that the aggregate index is the basic form of any general index; it can be converted to both the arithmetic mean and the harmonic mean indices.

The dynamics of turnover in the sale of industrial products should be characterized, as is known, by time series constructed over a number of past years, taking into account price changes (this applies, of course, to procurement, wholesale and retail turnover).

The index of sales volume (turnover), taken in prices of the corresponding years, has the form:

General price index:

General indexes- relative indicators obtained as a result of comparison of phenomena covering heterogeneous product groups.

General index of trade turnover (cost of marketable products);

where p1q1 is the turnover of the reporting period

p0q0 − turnover of the base period

p – prices, q – quantity

General price index: Ip =

Average indexes- these are relative indicators used to analyze structural changes. They are used only for homogeneous goods.

Price index of variable composition (average prices):

Constant price index:

6. The method of proportional division can be used in a number of cases to determine the magnitude of the influence of factors on the increase in the performance indicator . This applies to those cases when we are dealing with additive models Y=∑хi and models of multiple additive type:

In the first case, when we have a single-level model of type Y= a + b + c, the calculation is carried out as follows:

In multiple-additive type models, it is first necessary to determine, using a chain substitution method, how much the effective indicator has changed due to the numerator and denominator, and then calculate the influence of second-order factors using the method of proportional division using the above algorithms.

For example, the level of profitability increased by 8% due to an increase in the amount of profit by 1000 thousand rubles. At the same time, profit increased due to an increase in sales volume by 500 thousand rubles, due to an increase in prices - by 1,700 thousand rubles, and due to an increase in production costs, it decreased by 1,200 thousand rubles. Let's determine how the level of profitability has changed due to each factor:

7. To solve this type of problem, you can also use the equity method . To do this, first determine the share of each factor in the total amount of their increases (share ratio), which is then multiplied by the total increase in the performance indicator (Table 4.2):

Calculation of the influence of factors on the performance indicator using the equity method

8. The method of sequential isolation of factors is based on lies a method of scientific abstraction that allows one to study a large number of combinations with simultaneous changes in all or part of the factors.

The functioning of any socio-economic system (which includes an operating enterprise) occurs in conditions of complex interaction of a complex of internal and external factors. Factor- this is the cause, the driving force of a process or phenomenon, determining its character or one of its main features.

Under factor analysis understands the methodology for a comprehensive and systematic study and measurement of the impact of factors on the value of performance indicators.

In general, the following main ones can be distinguished: stages (tasks) factor analysis:

Setting the purpose of the analysis.

Selection of factors that determine the performance indicators under study.

Classification and systematization of factors in order to provide an integrated and systematic approach to the study of their influence on the results of economic activity.

Determination of the form of dependence between factors and the performance indicator.

Modeling the relationships between performance and factor indicators.

Calculation of the influence of factors and assessment of the role of each of them in changing the value of the performance indicator.

Working with the factor model (its practical use for managing economic processes).

In other words, method task- transition from a real large number of signs or causes determining the observed variability to a small number of the most important variables (factors) with minimal loss of information (methods that are similar in essence, but not in mathematical terms - component analysis, canonical analysis, etc.).

The method arose and was initially developed in problems of psychology and anthropology (at the turn of the 19th and 20th centuries), but now the scope of its application is much wider.

Purpose of factor analysis

Factor analysis- determining the influence of factors on the result - is one of the strongest methodological solutions in the analysis of the economic activities of companies for decision making. For managers - an additional argument, an additional “angle of view”.

The feasibility of using factor analysis

As you know, you can analyze everything ad infinitum. It is advisable at the first stage to implement an analysis of deviations, and where necessary and justified, to apply the factor analysis method. In many cases, a simple analysis of deviations is enough to understand that the deviation is “critical”, and when it is not at all necessary to know the degree of its influence.

Factors are divided into internal and external, depending on whether the activities of a given enterprise affect them or not. The analysis focuses on internal factors that the enterprise can influence.

Factors are divided into objective, independent of the will and desires of people, and subjective, influenced by the activities of legal entities and individuals.

According to the degree of prevalence, factors are divided into general and specific. Common factors operate in all sectors of the economy. Specific factors operate within a particular industry or a specific enterprise.

Types of factor analysis

The following types of factor analysis exist:

1) Deterministic (functional) – the effective indicator is presented in the form of a product, quotient or algebraic sum of factors.

2) Stochastic (correlation) - the relationship between the effective and factor indicators is incomplete or probabilistic.

3) Direct (deductive) – from the general to the specific.

4) Reverse (inductive) – from the particular to the general.

5) Single-stage and multi-stage.

6) Static and dynamic.

7) Retrospective and prospective.

Depending on the type of factor model, there are two main types of factor analysis - deterministic and stochastic.

Deterministic factor analysis is a technique for studying the influence of factors whose connection with the effective indicator is functional in nature, that is, when the effective indicator of the factor model is presented in the form of a product, quotient or algebraic sum of factors.

This type of factor analysis is the most common, since, being quite simple to use (compared to stochastic analysis), it allows you to understand the logic of the action of the main factors of enterprise development, quantify their influence, understand which factors and in what proportion it is possible and advisable to change to increase production efficiency.

Deterministic factor analysis has a fairly strict sequence of procedures:

1.building an economically sound deterministic factor model;

2. choosing a method of factor analysis and preparing conditions for its implementation;

3.implementation of counting procedures for model analysis;

Basic methods of deterministic factor analysis

Chain substitution method; Absolute difference method; Relative difference method; Integral method; Logarithm method.

Stochastic Analysis is a methodology for studying factors whose connection with a performance indicator, unlike a functional one, is incomplete and probabilistic (correlation). The essence of the stochastic method is to measure the influence of stochastic dependencies with uncertain and approximate factors. Stochastic method It is advisable to use for economic research with incomplete (probabilistic) correlation: for example, for marketing problems. If with a functional (complete) dependence with a change in the argument there is always a corresponding change in the function, then with a correlation connection a change in the argument can give several values ​​of the increase in the function depending on the combination of other factors that determine this indicator. For example, labor productivity at the same level of capital-labor ratio may be different at different enterprises. This depends on the optimal combination of other factors affecting this indicator.

Stochastic modeling is, to a certain extent, a complement and deepening of deterministic factor analysis. In factor analysis, these models are used according to three main reasons:

It is necessary to study the influence of factors for which it is impossible to build a strictly determined factor model (for example, the level of financial leverage);

It is necessary to study the influence of complex factors that cannot be combined in the same strictly deterministic model;

It is necessary to study the influence of complex factors that cannot be expressed in one quantitative indicator (for example, the level of scientific and technological progress).

It is also necessary to distinguish static And dynamic factor analysis. The first type is used when studying the influence of factors on performance indicators on the corresponding date. Another type is a technique for studying cause-and-effect relationships in dynamics.

Finally, factor analysis can be retrospective, which studies the reasons for the increase in performance indicators over past periods, and promising, which examines the behavior of factors and performance indicators in perspective.

Factor analysis can be single-stage or multi-stage. The first type is used to study factors of only one level (one level) of subordination without detailing them into their component parts. For example, . In multi-stage factor analysis, factors a and b are detailed into their component elements in order to study their behavior. The detailing of factors can be continued further. In this case, the influence of factors at different levels of subordination is studied.

It is also necessary to distinguish between static and dynamic factor analysis. The first type is used when studying the influence of factors on performance indicators on the corresponding date. Another type is a technique for studying cause-and-effect relationships in dynamics.

Galton F. (1822-1911), who also made a major contribution to the study of individual differences. But many scientists contributed to the development of Factor Analysis. The development and implementation of factor analysis in psychology was carried out by such scientists as Spearman Ch. (1904, 1927, 1946), Thurstone L. (1935, 1947, 1951) and Cattell R. (1946, 1947, 1951). It is also impossible not to mention the English mathematician and philosopher K. Pearson, who largely developed the ideas of F. Galton, and the American mathematician G. Hotelling, who developed a modern version of the principal component method. The English psychologist G. Eysenck, who widely used Factor Analysis to develop a psychological theory of personality, also deserves attention. Mathematically, factor analysis was developed by Hotelling, Harman, Kaiser, Thurstone, Tucker, etc. Today, factor analysis is included in all statistical data processing packages - SAS, SPSS, Statistica, etc.

Tasks and possibilities of factor analysis

Factor analysis allows you to solve two important problems for the researcher: to describe the object of measurement comprehensively and at the same time compact. Using factor analysis, it is possible to identify hidden variable factors responsible for the presence of linear statistical relationships of correlations between observed variables.

Thus, two goals of Factor Analysis can be distinguished:

During the analysis, variables that are highly correlated with each other are combined into one factor, as a result, the variance is redistributed between the components and the most simple and clear structure of factors is obtained. After combining, the correlation of components within each factor with each other will be higher than their correlation with components from other factors. This procedure also makes it possible to isolate latent variables, which is especially important when analyzing social ideas and values. For example, when analyzing scores obtained on several scales, a researcher notices that they are similar to each other and have a high correlation coefficient, he can assume that there is some latent variable that can be used to explain the observed similarity of the scores obtained. This latent variable is called factor. This factor influences numerous indicators of other variables, which leads us to the possibility and necessity of identifying it as the most general, of a higher order. To identify the most significant factors and, as a consequence, the factor structure, it is most justified to use the principal components method (PCA). The essence of this method is to replace correlated components with uncorrelated factors. Another important characteristic of the method is the ability to limit oneself to the most informative principal components and exclude the rest from the analysis, which simplifies the interpretation of the results. The advantage of PCA is also that it is the only mathematically based method of factor analysis.

Factor analysis can be:

• exploration- it is carried out when studying the latent factor structure without assumptions about the number of factors and their loadings;
• confirmation, designed to test hypotheses about the number of factors and their loadings (note 2).

Conditions for using factor analysis

The practical implementation of factor analysis begins with checking its conditions. The mandatory conditions of factor analysis include:

Basic concepts of factor analysis

• Factor - hidden variable
• Loading - correlation between the original variable and the factor

Rotation procedure. Isolation and interpretation of factors

The essence of factor analysis is the procedure for rotating factors, that is, redistributing variance according to a certain method. The purpose of orthogonal rotations is to determine the simple structure of factor loadings, the purpose of most oblique rotations is to determine the simple structure of secondary factors, that is, oblique rotations should be used in special cases. Therefore, orthogonal rotation is preferable. According to Muljek's definition, a simple structure meets the requirements:

• each row of the secondary structure matrix V must contain at least one zero element;
• For each column k of the secondary structure matrix V there must be a subset of r linearly independent observed variables whose correlations with the kth secondary factor are zero. This criterion boils down to the fact that each column of the matrix must contain at least r zeros.
• One of the columns of each pair of columns of the matrix V must have several zero coefficients (loadings) in those positions where they are non-zero for the other column. This assumption guarantees the distinguishability of the secondary axes and their corresponding subspaces of dimension r-1 in the space of common factors.
• When the number of common factors is greater than four, each pair of columns should have a number of zero loadings in the same rows. This assumption makes it possible to divide the observed variables into separate clusters.
• For each pair of columns of matrix V there should be as few significant loadings corresponding to the same rows as possible. This requirement ensures that the complexity of the variables is minimized.

(In Mullake's definition, r denotes the number of common factors, and V is the secondary structure matrix formed by the coordinates (loads) of the secondary factors obtained as a result of rotation.) Rotation occurs:

• orthogonal
• oblique.

In the first type of rotation, each subsequent factor is determined in such a way as to maximize the variability remaining from the previous ones, so the factors turn out to be independent and uncorrelated from each other (PCA belongs to this type). The second type is a transformation in which factors are correlated with each other. The advantage of oblique rotation is the following: when it results in orthogonal factors, you can be sure that this orthogonality is really inherent in them, and not artificially introduced. There are about 13 methods of rotation in both types, five are available in the statistical program SPSS 10: three orthogonal, one oblique and one combined, but of all the most common is the orthogonal method " varimax" The varimax method maximizes the spread of squared loadings for each factor, resulting in larger and smaller factor loadings. As a result, a simple structure is obtained for each factor separately.

The main problem of factor analysis is the identification and interpretation of the main factors. When selecting components, the researcher usually faces significant difficulties, since there is no unambiguous criterion for identifying factors, and therefore subjectivity in the interpretation of the results is inevitable. There are several commonly used criteria for determining the number of factors. Some of them are alternative to others, and some of these criteria can be used together so that one complements the other:

Practice shows that if rotation does not produce significant changes in the structure of the factor space, this indicates its stability and the stability of the data. There are two more options: 1). strong redistribution of variance is the result of identifying a latent factor; 2). a very slight change (tenths, hundredths or thousandths of the load) or its absence at all, while only one factor can have strong correlations - a single-factor distribution. The latter is possible, for example, when several social groups are checked for the presence of a certain property, but only one of them has the desired property.

Factors have two characteristics: the amount of variance explained and loadings. If we consider them from the point of view of geometric analogy, then regarding the first we note that the factor lying along the OX axis can explain a maximum of 70% of the variance (the first main factor), the factor lying along the OU axis can determine no more than 30% (the second main factor). That is, in an ideal situation, all the variance can be explained by two main factors with the indicated shares. In a normal situation, two or more main factors may be observed, and there remains a portion of uninterpretable variance (geometric distortions) that is excluded from the analysis due to insignificance. Loadings, again from the point of view of geometry, are projections from points on the OX and OU axes (with a three or more factor structure also on the OZ axis). Projections are correlation coefficients, points are observations, so factor loadings are measures of association. Since a correlation with a Pearson coefficient R ≥ 0.7 is considered strong, only strong connections should be paid attention to in the loads. Factor loadings can have the property bipolarity- the presence of positive and negative indicators in one factor. If bipolarity is present, then the indicators included in the factor are dichotomous and are in opposite coordinates.

Factor analysis methods:

Notes

Literature

• Afifi A., Eisen S. Statistical analysis: Computer approach. - M.: Mir, 1982. - P. 488.
• Colin Cooper. Individual differences. - M.: Aspect Press, 2000. - 527 p.
• Gusev A. N., Izmailov Ch. A., Mikhalevskaya M. B. Measurement in psychology. - M.: Smysl, 1997. - 287 p.
• Mitina O. V., Mikhailovskaya I. B. Factor analysis for psychologists. - M.: Educational and methodological collector Psychology, 2001. - 169 p.
• Factor, discriminant and cluster analysis / collection of works, ed. Enyukova I. S.- M.: Finance and Statistics, 1989. - 215 p.
• Patsiorkovsky V.V., Patsiorkovskaya V.V. SPSS for sociologists. - M.: Textbook of ISEPN RAS, 2005. - 433 p.
• Büül A., Zöfel P. SPSS: The Art of Information Processing. Analysis of statistical data and recovery of hidden patterns. - St. Petersburg: DiaSoftYUP LLC, 2002. - 603 p.
• Factor, discriminant and cluster analysis: Transl.

F18 from English/J.-O. Kim, C. W. Mueller, W. R. Klekka, etc.; Ed. I. S. Enyukova. - M.: Finance and Statistics, 1989.- 215 p.:

Links

• Electronic textbook StatSoft. Principal components and factor analysis
• Nonlinear principal component method (library website)

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See what “Factor analysis” is in other dictionaries:

factor analysis- - factor analysis The field of mathematical statistics (one of the sections of multivariate statistical analysis), combining computational methods that in some cases allow ... Technical Translator's Guide

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factor analysis- (from Latin factor active, producing and Greek analysis decomposition, division) a method of multidimensional mathematical statistics (see statistical methods in psychology), used in the study of statistically related characteristics with the aim of ... ... Great psychological encyclopedia

A method for studying economics and production, which is based on an analysis of the impact of various factors on the results of economic activity and its effectiveness. Raizberg B.A., Lozovsky L.Sh., Starodubtseva E.B.. Modern economic ... Economic dictionary

Factor analysis- the field of mathematical statistics (one of the sections of multivariate statistical analysis), combining computational methods, which in some cases make it possible to obtain a compact description of the phenomena under study based on... ... Economic and mathematical dictionary

FACTOR ANALYSIS, in statistics and psychometrics, a mathematical method by which a large number of measurements and studies are reduced to a small number of “factors” that fully explain the research results, as well as their... ... Scientific and technical encyclopedic dictionary

Multivariate statistical analysis section (See Multivariate statistical analysis). combining methods for estimating the dimension of a set of observed variables by examining the structure of covariance or correlation matrices.... ... Great Soviet Encyclopedia

Conducting factor analysis of finance. results are carried out based on several indicators:

• Profit from sale;
• Net profit;
• Gross profit;
• Profits before taxes.

Let's look at how each of these indicators is analyzed in more detail.

Factor analysis of sales profit

Factor analysis is a method of complex and systematic measurement and study of the influence of factors on the size of the final indicators. It is carried out on the basis of accounting. report on the second form.

The main purpose of such an analysis is to find ways to increase the profitability of the company.

The main factors that influence profit margins are:

1. Product sales volume. To find out how it affects profitability, you need to multiply the change in the number of goods sold by the profit of the previous reporting period.
2. Variety of products sold. To find out its impact, you need to compare the profit of the current period, which is calculated based on the cost and prices of the base period, with the base profit, recalculated for the change in the number of products sold.
3. Change in cost. To find out its impact, you need to compare the cost of sales of goods in the reporting period with the costs of the base period, which are recalculated for changes in the level of sales.
4. Commercial and administrative costs. Their impact is calculated by comparing their sizes in the base period and the reporting period.
5. Price level. To find out its impact, you need to compare the sales level of the reporting period and the base period.

Factor analysis of sales profit - calculation example

Background information:

The factors listed above had the following impact on profit:

1. Volume of products sold – -1578 thousand rubles.
2. Variety of goods sold – -1373 thousand rubles.
3. Cost – -5679 thousand rubles.
4. Commercial costs – +1140 thousand rubles.
5. Administrative costs – +1051 thousand rubles.
6. Prices – +7068 thousand rubles.
7. Influence of all factors – +630 thousand rubles.

Factor analysis of net profit

Conducting factor analysis of net profit occurs in several stages:

1. Determination of profit change: PE = PE1 – PE0
2. Calculation of sales growth: B%= (B1/B0)*100-100
3. Determining the impact of changes in sales on profit: NP1= (NP0*B%)/100
4. Calculation of the impact of price changes on profit: PE1=(B1-B0)/100
5. Determining the impact of changes in cost: PP1= (s/s1 – s/s0)/100

Factor analysis of net profit - calculation example

Initial information for analysis:

Let's analyze:

1. Profit decreased by 3,000 thousand rubles.
2. The sales level fell by 25.58%, which amounted to 1,394 thousand rubles.
3. The impact of changes in the price level amounted to 9,000 thousand rubles.
4. Impact of cost - 11850 thousand rubles.

Factor analysis of gross profit

Gross profit is the difference between the profit from the sale of goods and their cost. Factor analysis of gross profit is carried out on the basis of accounting. report on the second form.

The change in gross profit is influenced by:

• Change in the number of goods sold;
• Changes in product costs.

Factor analysis of gross profit - example

Initial information is given in the table:

Substituting the initial data into the formula, we find that the impact of changes in revenue amounted to 1,686 thousand rubles.

Factor analysis of profit before tax

Factors that influence profit before taxes are as follows:

• Change in the quantity of goods sold;
• Change in the structure of sales;
• Changes in prices for goods sold;
• Commercial and administrative costs;
• Cost price;
• Changes in prices for resources that make up the cost.

Factor analysis of profit before tax - example

Let's consider an example of analyzing profits before taxes.

From the table we can draw conclusions:

1. Profit before taxes in the reporting period compared to the base period decreased by 157,047 thousand rubles. This was mainly due to a decrease in profit margins from product sales.
2. In addition, a decrease in interest receivable (by 2,700 thousand rubles) and other income (by 22,900 thousand rubles) had a negative impact.
3. Only the reduction in other costs (by 5,400 thousand rubles) had a positive effect on profit before taxes.