JP5120820B2 - Equipment that evaluates appropriate standard residential land by regression analysis that eliminates "multicollinearity" - Google Patents

Description

  The present invention is an apparatus that performs an appropriate evaluation of a standard residential land.

  The transaction case comparison method, which is the main method of appraisal evaluation of residential land, obtains the price of the target site by comparing the transaction case price in the neighborhood with the price formation factor. However, it cannot be said that the parties of the residential land transaction are familiar with the land market, and because it depends on the circumstances of the individual, the established price often deviates from the price that seems to be appropriate for the residential land, We cannot expect an appropriate price gap for the transaction case price.

  The “land price ratio table” has been published as the price disparity evaluation standard, and the land price survey is conducted annually by the Land Price Public Notice Act and the Land Use Plan Act Enforcement Order, which serves as a guideline for evaluation. . However, these public evaluations are price indications only, and although there is a guarantee of the price as a result of an expert appraisal by an expert appraiser, it is objective and rational due to price formation factors regarding price differences between standard sites. The grounds are not specified.

  The evaluation of residential land must be based on price formation factors, but the basis for the evaluation is clarified when the appropriate price disparity is calculated for many and various residential land, as in the standard residential land evaluation for residential land taxation. In order to achieve this, a multiple regression analysis is performed using the price formation factor as an explanatory variable and the primarily evaluated price as an objective variable.

  The multiple regression analysis is to find out how much the explanatory variables of the group can explain the objective variable as a whole, and does not aim at how much the individual explanatory variables can explain the objective variable independently.

  However, in the appraisal evaluation of residential land, it is required how much the land price difference, which is an explanatory variable, has an explanatory power of the land price difference with respect to the land price which is the objective variable. However, in multiple regression analysis of land prices, there are many cases in which there is a high correlation between the price formation factors that make up the normal equation, and the partial regression coefficient of each factor that indicates the extent to which land prices can be explained is based on numerical values based on the experience of appraisal evaluation. A dissociating “multicollinearity” problem arises.

The solution to “multicollinearity” is to omit one of the two explanatory variables with a high correlation coefficient, but it is not acceptable if it is the main price-forming factor selected by theory and experience. In addition, there is a method in the following paper to obtain a stable partial regression coefficient by adding a certain number to the diagonal elements of the correlation matrix, but it is a mechanical operation and the basis for where to stop adding the numerical value is ambiguous There are criticisms.
Arthur E.M. Hoer and Robert W. Kennard
“Ridge regression”

The present invention
Add the total value (%) for each price formation factor of many standard sites to the standard value of 1 to give a rating value of (1 + total value), and enter this and the standard site set price into the computer Means for creating a database (p is the price, the price formation factor is street a, approach b, environment c)
Taking the logarithm with the price as the objective variable and the price formation factor rating value as the explanatory variable, calculate the standardized variable Ap of the objective variable and the standardized variable Ai (i = a, b, c) of the explanatory variable, and explain the objective variable Means for calculating correlation coefficients Ri and rij between variables and explanatory variables;
For all combinations of three variables of Ai including Ap of each standard place (i = (p, a, b), (p, a, c), (p, b, c)) Means for distinguishing Ap, Ai (synchronization) being the same from asynchronous Ap ′, Ai ′;
For example, if the combination of three variables is Ap, Aa, Ab, the numerical value comparison is first performed for Ap and Aa. Means to remove from Aa as a tuning part,
The ratio of the sum of the absolute values of the tuning Aa before the removal and the sum of the absolute values after the removal is obtained, and in order to balance the values of the tuning Aa and the non-tuning Aa ', the correction Ata is obtained by multiplying both the values of the Aa before removal. means,
Means for performing the same calculation for Ap and Ab, obtaining the correction Atb, multiplying the correction Ata and the correction Atb, and obtaining the correlation coefficient lab of the factors a and b,
Means for performing the previous calculation for all other three variable combinations, obtaining rac and rbc, creating a correlation matrix, and creating a ternary simultaneous equation in the normal equation format of multiple correlation analysis;
Means for solving the ternary simultaneous equations, obtaining a partial regression coefficient of each explanatory variable, obtaining a logarithmic regression price from a linear expression of the objective variable based on the partial regression coefficient, and reducing the logarithm to obtain a price of the objective variable;
Means to make the calculated regression price the same level as the average value and standard deviation of the default price
It is related with the apparatus which calculates | requires the final price of the standard residential land characterized by having provided.

ここで、
Ｒｉ ：要因ｉの目的変数ｙに対する単相関係数
ｒｉｊ：相関行列における要因ｉ，ｊの非対角要素 （ｉ≠ｊ，ｉ、ｊ＝１〜３）
ｂｉ ：変数標準化後のｉ要因の係数
なお、変数標準化前後のｂ’ｉ、ｂｉの関係は次のとおりである。
ｂ’ｉ＝ｂｉ（σｙ／σｉ） （２）
ｂｉ：標準化後の係数 ｂ’ｉ：標準化前の係数
σｙ：目的変数ｙの標準偏差
σｉ：説明変数ｉの標準偏差
（１）式の第一行は次のとおりである。
ｂ１＋ｂ２・ｒ１２＋ｂ３・ｒ２３＝Ｒ１ （３）
この式の意味するのは、右辺の要因１の目的変数ｙに対する単相関係数Ｒ１は、要因１の要因ｉに対する相関係数ｒ１ｉ（自己相関を含む）に、目的変数に対する要因ｉの説明能力度係数であるｂｉを乗じたものの総和であるということである。これは、ｙの説明に要因１以外の他の要因ｉが関わる場合は、要因１だけでなく、関わりのある他の説明変数ｉの作用が加わることを意味する。
ｂｉはＲｉに対する要因ｉの説明能力度比重であるので、第１行のｒ１ｉは要因１により生成されたｉ要因（このような意味での相関）と解され、また、その生成に見合う程度で要因１のｙに対する説明を部分的に担っていると解される。
そして、この（３）式で、相関行列の対角要素である自己相関の１に比して、非対角要素であるｒ１ｉの数値の和が大きい場合には、これら２次的要因の作用で、ｂ１の値はＲ１の数値から大きく離れ、多重共線性問題を生じさせる。If the normal equations related to the objective variable and explanatory variable of the multiple regression analysis are displayed as a correlation matrix, it becomes as follows. (In the case of explanatory variable 3)

here,
Ri: single correlation coefficient for objective variable y of factor i rij: off-diagonal element of factors i, j in correlation matrix (i ≠ j, i, j = 1-3)
bi: coefficient of i factor after variable standardization The relationship between b′i and bi before and after variable standardization is as follows.
b′i = bi (σy / σi) (2)
bi: Coefficient after standardization b′i: Coefficient before standardization σy: Standard deviation of objective variable y σi: Standard deviation of explanatory variable i The first line of equation (1) is as follows.
b1 + b2 · r12 + b3 · r23 = R1 (3)
This equation means that the single correlation coefficient R1 for the objective variable y of the factor 1 on the right side is the explanatory coefficient of the factor i for the objective variable to the correlation coefficient r1i (including autocorrelation) for the factor i of the factor 1. That is, it is the sum of products multiplied by bi which is a degree coefficient. This means that when the factor i other than the factor 1 is involved in the explanation of y, not only the factor 1 but also other explanatory variables i that are related are added.
Since bi is the explanation ability degree specific gravity of the factor i with respect to Ri, r1i in the first row is interpreted as the i factor (correlation in this sense) generated by the factor 1, and is appropriate to the generation. It is understood that it is partially responsible for the explanation of factor 1 y.
If the sum of numerical values of r1i that is a non-diagonal element is larger than the autocorrelation 1 that is a diagonal element of the correlation matrix in the equation (3), the action of these secondary factors Thus, the value of b1 is far from the value of R1 and causes a multicollinearity problem.

In order to calculate the correlation coefficient Ri between the objective variable y and the explanatory variable xi and the correlation coefficient rij between the explanatory variables in the multiple regression analysis of 3 explanatory variables, the standardized variables Ayα and Aiα are calculated for each sample α. However, when they are compared for each sample, positive and negative signs and high synchrony are recognized in numerical values.
(In order to avoid complications, α is not displayed to indicate individual specimens except when misleading.)
The single correlation coefficient Ri indicates the degree to which the explanatory variable i can explain the objective variable y (correlation in this sense), but is obtained independently of other explanatory variables. On the other hand, the value of Ri increases as the degree of synchronization of the sign and numerical values of the standardized variables Ay and Ai of the objective variable y and the explanatory variable xi increases. The explanatory variables i and j selected as having high explanatory ability for y have a low correlation between i and j, but if the synchronism of the signs and values of Ai and Aj to Ay is high, Ai, Aj's mutual sign and numerical synchrony are enhanced.
From this, rij of the correlation matrix of the multiple regression analysis is mediated by the part where the factors i and j are directly correlated and the single correlation coefficients Ri and Rj for the objective variable y of the factors i and j. In other words, there is a part that increases the correlation in appearance. The direct correlation of the i and j factors should be incorporated in some way if the causal basis is clear, but ignored if the causal basis is clear. If the apparent correlation mediated by the objective variable is removed, the value of rij is suppressed, which leads to elimination of “multicollinearity”.

When p is a price, a, b, c are three conditions of a price forming factor, a street, an approach, and an environment, in order to remove the synchrony with respect to the standardized variables Ap, Ai (i = a, b, c), Two aspects of positive and negative sign tuning and numerical tuning must be analyzed.
The sign tuning is the same for all three combinations of Ai including Ap (i = (p, a, b), (p, a, c), (p, b, c)). Find out. Each of Ap and Ai of each sample is 1 in the case of + sign, and -1 in the case of-sign, and when the sum of them is 3 and -3, the sign of three variables coincides. Gives the number of.
The device according to the present invention has all combinations of three variables of factor Ai including Ap of each standard place (i = (p, a, b), (p, a, c), (p, b, c)). Are provided with means for distinguishing Ai (synchrony), which are all the same sign, from Ai ′ (nonsynchrony), which are all different signs.

Regarding the tuning of numerical values, in the case of Ap, Aa, Ab, which is one of the combinations of three variables having the same sign, the objective variable Ap and the explanatory variable Aa are first taken up, and the numerical tuning of Aa mediated by the objective variable Ap is performed. The part is removed up to the lower of the absolute values of Ap and Aa.
Example of removal Ap Aa (tuned portion) (natural portion) residual 0.3 0.3 0.3 0
0.2 0.5 0.2 0.3
-0.6 -0.4 -0.4 0
-0.1 -0.4 -0.1 -0.3
For example, when the combination of three variables is Ap, Aa, and Ab, the apparatus of the present invention first takes Ap and Aa, compares the values, and sets a numerical value with a low absolute value as the target variable. Means are provided for removal from Aa as a p-mediated tuning moiety.

When Ap and Aa of individual samples are compared, there is a considerable difference in the corresponding numerical values, and the degree of tuning is unstable, so that there is only a certain degree of tuning as a whole.
Therefore, for the sample Aa selected as tuned, in order to balance the values of tuned Aa and unsynchronized Aa ′, the absolute value of the remaining part (hereinafter referred to as the eigen part) from which the Ap-mediated tuned effect has been removed. Is obtained by multiplying the tuned and non-tuned samples Aa and Aa ′ before removal of the tuned portion by the ratio of the absolute value of Aa before removal of the tuned degree, and multiplying them by the sample Ai after removal (corrected Ati) Said).
The same calculation as described above is performed for Ap and Ab to obtain a corrected Atb.
The calculation so far is performed for all three combinations of Ai including Ap to obtain correction Ati, and the partial regression coefficient is obtained using the synergistic sum of the non-diagonal elements lab, rac, and rbc of the correlation matrix, and the regression price Is calculated.

Since the apparatus of the present invention balances the numerical values of the synchrony Aa and the non-synchronization Aa ′ with the combination of Ap and Aa, the sum of the absolute values of the synchronism Aa before the removal is equal to the sum of the absolute values of the synchronism Aa before the removal. Means are provided for determining the ratio and multiplying the tuned / unsynchronized Aa value before removal to obtain the corrected Ata.
Further, the apparatus of the present invention includes means for calculating a non-diagonal element lab of the correlation matrix by multiplying the obtained correction Ata and correction Atb for the combination of Ap, Aa, and Ab.

Since the regression price obtained by this calculation is different from the normal multiple regression analysis calculation, it may be far from the average value of the default price and the standard deviation value. In order to correct the price and the price difference level, the average value of the initial setting price and the price equal to the standard deviation are corrected.
The apparatus of the present invention comprises means for obtaining a final price that makes the regression price obtained by the correlation matrix after removal of the tuning part the same level as the average value and standard deviation of the initial setting price.

The above procedure is for Ap and Ai of individual standard sites, but is somewhat complicated.
In the simplified method 1, the higher the numerical value of the i-factor single correlation coefficient Ri, the higher the sign and numerical values of Ap and Ai are considered to be synchronized. Ai · (1-Ri) collectively removed from A is defined as Ai after the synchrony removal, and rij (1-Ri) (1-Rj), which is synergistic with Aj obtained from the same calculation for each factor, is This is a method for obtaining a partial regression coefficient as a non-diagonal element. In addition, the simplified method 2 has no theoretically or empirically significant correlation between the price forming factors i and j, and the correlation between the correlation coefficients Ri and Rj is Therefore, there is a method for calculating the partial regression coefficient with the correlation coefficient rij as 0 when the factors i and j are considered to be strongly synchronized with the objective variable.

The apparatus of the present invention uses the single correlation coefficient Ri of the objective variable p and the explanatory variable i as a tuned equivalent, and synergistic rij (1-Ri) of each factor of Ai (1-Ri) obtained by batch removal from Ai. ) A simple method 1 calculating means for calculating a partial regression coefficient with a correlation matrix having (1-Rj) as a non-diagonal element is provided.
In addition, since the device of the present invention has no theoretically or empirically significant correlation between the price forming factors, and the single correlation coefficients Ri and Rj are high numerical values, the i and j factors are mutually Ap-mediated. When a high correlation is considered, a simple method 2 calculating means for obtaining a partial regression coefficient by setting the correlation coefficient rij of these explanatory variables to 0 is provided.

  By eliminating the standardized objective variable Ap-mediated tuning correlation from the standardized explanatory variables Ai and Aj of the components of rij that are non-diagonal elements of the correlation matrix, "multicollinearity" is eliminated, and price formation It is possible to obtain a partial regression coefficient that shows an appropriate price explanation of the factors, and by using the regression price as the initial price price and the price disparity level, it is necessary to obtain rational evaluation materials that are directly linked to the appraisal practice. .

FIG. 2 is a table of set prices and rating values of price formation factors (street, approach, environment). In the appraisal evaluation, the residential land serving as a reference for comparison is set to 1, and the percentage of the utility of the target land is compared to the lower or higher, so the evaluation formula has the form (1 + xi). Note that the set price is obtained by a normal appraisal method.

FIG. 3 is a calculation table of Ap, Ai and AiAj, Ri by logarithm of objective variable (price) and explanatory variable (price formation factor) and standardization of variables. Since the comparison of standard sites is not the difference in the following ratio, when applying regression analysis which is a linear format, the calculation is performed with the logarithm of the variable.
(P1 / p2) = (1 + x1) / (1 + x2)
Logarithm log (p1 / p2) = log (p1) −log (p2) (4)
p1: Evaluation target site
p2: Evaluation standard site The standardization of variables is as follows.
Aiα = (Xiα−Xi average) / σi (5)
Here, Xiα: i factor evaluation value of α sample σi: standard deviation of i factor The correlation coefficient rij of i, j factor, and the single correlation coefficient Ri for the objective variable p of i factor are as follows.
rij = 1 / n × Σ {(Xiα−Xi average) (Xjα−Xj average)} / σiσj
= 1 / n × ΣAiαAjα
Ri = 1 / n × ΣAiαApα

Related to FIG. 4 The synchrony analysis of standardized variables Ap and Ai is performed by combining all three variables of Ai including Ap (i: (p, a, b), (p, a, c), (p, b, c). Check if the sign of)) is the same. Each of Ap and Ai is given a value of 1 for tuning, assuming 1 for a + sign and -1 for a-sign, and 3 or -3 when the sum is 3 or -3.

5 and 6
The removal of the tuned portion of the Aa of the tuned sample is removed from the value of Aa up to a value having a lower absolute value of Ap and Aa compared to Ap. In order to balance the Aa values after tuning and non-tuning, the ratio of the sum of absolute values after removal to the sum of absolute values before removal of tuning Aa is multiplied by Aa before removal regardless of tuning or non-tuning. The correction Ata is obtained.
The correlation coefficient lab of the factors a and b is obtained by multiplying the correction Atb obtained by the same calculation and the previous correction Ata. This calculation is performed for all three variable combinations.

7 A partial regression coefficient is obtained from the correlation matrix of the correlation coefficient rij (i, j = a, b, c) after removal obtained in the previous stage, and a partial regression coefficient after removal of the tuning portion is obtained.

Related to Fig. 8: Calculate the regression price and correlation coefficient after removal of the tuning part. In order to keep the calculated regression price at the price of the initial setting price and the level of the price gap, the regression price is corrected to the regression price that is the same as the average value and standard deviation of the setting price.

Relevant to FIG. 9 The regression analysis for eliminating the “multiple collinearity” described above removes the synchrony portion of each specimen, but is somewhat complicated. The simple method 1 considers the single correlation coefficient Ri of the price formation factor i, which is the set price p and the explanatory variable, as the equivalent of the synchronization of the objective variable, and removes it from the standardized variable Ai of the factor i at a time. This is a calculation for obtaining a partial regression coefficient, with -Ri) as Ai after the removal of synchrony and the synergistic sum of the combinations of these factors as rij of the off-diagonal elements of the correlation matrix.

Relevant to Fig. 9 Since the simple method 2 has no theoretically or empirically significant correlation between the price formation factors and the correlation coefficients Ri and Rj are highly correlated, the factors i and j are highly synchronized with the objective variable. In this case, the partial regression coefficient is calculated by setting the correlation coefficient of the i and j factors to rij = 0.

Multiple regression analysis flowchart to eliminate "multicollinearity" Objective variable (price) and explanatory variable (price formation factor) data Logarithm and standardization of variables (Aiα) and calculation of AiAj, Ri Synchrony analysis of positive and negative signs of three variables of Ai including Ap The numerical tuning part with Ap is removed from Aa of the three variables (Ap, Aa, Ab) of positive / negative sign tuning-Calculation of correction Ata- The numerical tuning part with Ap is removed from Ab of three variables (Ap, Aa, Ab) of positive / negative sign tuning and calculation of correlation coefficient of Aa, Ab-Calculation of corrected Ata and rab- Calculation of partial regression coefficient after initial input and tuning part removal Regression price after removal of tuned part, calculation of correlation coefficient, and correction of regression price to the same value as the average value and standard deviation of the default price Calculation of partial regression coefficients using simplified methods 1 and 2

Claims (8)

Add the total value (%) for each price formation factor of many standard sites to the standard value of 1 to give a rating value of (1 + total value), and enter this and the standard site set price into the computer Means for creating a database (p is the price, the price formation factor is street a, approach b, environment c)
Taking the logarithm with the price as the objective variable and the price formation factor rating value as the explanatory variable, the standardized variable Ap of the objective variable and the standardized variable Ai (i = a, b, c) of the explanatory variable are calculated, and the objective variable and explanation Means for calculating correlation coefficients Ri and rij between variables and explanatory variables;
For all combinations of three variables of Ai including Ap of each standard place (i = (p, a, b), (p, a, c ), (p, b, c)) Means for distinguishing Ap, Ai (synchronization) being the same from asynchronous Ap ′, Ai ′;
For example, if the combination of three variables is Ap, Aa, Ab, the numerical value comparison is first performed for Ap and Aa. Means to remove from Aa as a tuning part,
The ratio of the sum of the absolute values of the tuning Aa before removal and the sum of the absolute values after removal is obtained, and in order to balance the numerical values of the tuning Aa and the non-tuning Aa ′, the correction Ata is obtained by multiplying both of the Aa values before removal. means,
Means for performing the same calculation for Ap and Ab, obtaining the correction Atb, multiplying the correction Ata and the correction Atb, and obtaining the correlation coefficient lab of the factors a and b,
Means for performing the previous calculation for all other three variable combinations, obtaining rac and rbc, creating a correlation matrix, and creating a ternary simultaneous equation in the normal equation format of multiple correlation analysis;
Means for solving the ternary simultaneous equations, obtaining a partial regression coefficient of each explanatory variable, obtaining a logarithmic regression price from a linear expression of the objective variable based on the partial regression coefficient, and reducing the logarithm to obtain a price of the objective variable;
Means to make the calculated regression price the same level as the average value and standard deviation of the default price
A device that calculates the final price of a standard residential land characterized by having The signs of all the combinations of the three variables of the factor Ai including Ap of each standard place (i = (p, a, b), (p, a, c), (p, b, c)) are all 2. An apparatus according to claim 1, comprising means for distinguishing Ai (tunability) of the same sign from Ai ′ (non-tunability) of which are different signs. For example, if the combination of three variables is Ap, Aa, Ab, for the synchronization standard place, first take Ap and Aa and compare their numerical values. The apparatus of claim 1 comprising means for removal from Aa. In order to balance the numerical values of the synchrony Aa and the non-synchronization Aa ′ with the combination of Ap and Aa, the ratio of the sum of the absolute values after the removal to the sum of the absolute values of the synchrony Aa before the removal is obtained, The apparatus of claim 1, further comprising means for multiplying the unsynchronized pre-removal Aa value to determine a corrected Ata. The apparatus according to claim 1, further comprising means for calculating a non-diagonal element lab of the correlation matrix by multiplying the obtained correction Ata and the correction Atb for the combination of Ap, Aa, and Ab. The apparatus according to claim 1, further comprising means for obtaining a final price at which the regression price obtained by the correlation matrix after removal of the tuning part is the same level as the average value and standard deviation of the initial setting price. A single correlation coefficient Ri between the objective variable p and the explanatory variable i is used as a tuned equivalent, and a synergistic rij (1-Ri) (1-Rj) of each factor of Ai (1-Ri) obtained by collectively removing from Ai. The apparatus according to claim 1, further comprising a simple method 1 calculating means for calculating a partial regression coefficient using a correlation matrix having a non-diagonal element as a diagonal element . If there is no theoretically or empirically significant correlation between price formation factors, and the single correlation coefficient Ri, Rj is a high value, if there is a high Ap-mediated correlation between i, j factors The apparatus according to claim 1, further comprising a calculating means of a simple method 2 for obtaining a partial regression coefficient with a correlation coefficient rij of the explanatory variable of 0 as 0.

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