The analysis process of the panel data entropy method is as follows:
1. Case background
There are currently 9 companies with financial indicator data for 5 consecutive years (2018-2022), and I want to use this data to determine the weight of each financial indicator. The entropy value method determines the size of the weighting according to the degree of dispersion of the indicators, which is objective, fair and accurate. There are not many indicator data collected this time, so choosing the entropy value method to determine the indicator weight has strong operability, and the calculation process is simple and easy to operate.
The data is the data of 5 financial indicators of 9 companies for 5 consecutive years. Because it contains both time series data and cross-sectional data, it belongs to panel data. There should be 9*5=45 rows of data, each of the 5 financial indicators occupies a column, and the company number and year each occupy a column. Finally, there should be 45 rows*7 columns of data. Finally, the data should be organized into the following format:
Data fictitious, only for teaching demonstration
2. Data processing
Using the entropy method for analysis requires data processing, including data direction processing and data dimension processing.
(1) Direction processing
The five indicators of this analysis are operating profit, total assets, total liabilities, current ratio, and cost of sales. It can be seen that these five indicators include both positive indicators (the bigger the better, such as profit), and reverse indicators (the smaller the better, such as cost). In the operation rules of the entropy value method, the larger the forward index, the better, and the smaller the reverse index, the better, so the data needs to be processed in the direction.
The positive indicators "operating profit", "total assets" and "current ratio" are positively processed by SPSSAU; the reverse indicators "total liabilities" and "cost of sales" are reversely processed by SPSSAU.
SPSSAU [Generate Variables] -> Forward/Reverse -> Confirmation processing, the operation is as shown in the figure below:
Similarly, the other two indicators can be reversed.
(2) Dimensional processing
After the entropy value method eliminates the influence of the data direction, it is also necessary to eliminate the influence caused by the different data units, that is, perform dimensional processing. SPSSAU provides more than a dozen dimensional processing methods. Here, it is recommended to use data normalization for processing.
In this case, because the forward/reverse processing has been carried out in the above analysis, and the forward/reverse processing can solve the problem of direction and dimension at the same time, so there is no need to perform normalization processing again. After the data processing is completed, the operation instructions of the panel entropy method will be carried out next.
3. Panel entropy method operation
The entropy value method determines the weight according to the entropy value. "Entropy" was originally a concept of thermodynamics, and was later introduced into information theory to objectively determine weights. The principle of entropy is to judge the weight by the degree of dispersion of the index. The greater the degree of dispersion, the more uncertain factors, the greater the impact on the evaluation results, and the greater the weight.
From the perspective of the calculation principle of entropy value, it does not consider whether it is panel data, panel data is exactly the same as ordinary data, and can be directly analyzed.
From an analysis point of view, for panel data, the entropy method can be analyzed from two perspectives, as shown in the following table:
Next, two methods are used to describe the operation of the panel data entropy method.
(1) One-time method
In the SPSSAU system, comprehensive evaluation [entropy method] -> drag all the processed data into the analysis box -> non-negative translation -> start analysis
The weight obtained at this time is the index weight obtained by directly calculating the entropy method once without distinguishing whether it is panel data or not.
Supplementary non-negative translation: For data that has been forwarded/reversed/standardized, the index data range can be taken to 0, but the logarithmic calculation will be performed when calculating the entropy weight, and the appearance of 0 will make the calculation meaningless, so the overall data needs to be calculated Do a non-negative translation. The non-negative translation function of SPSSAU means that if the data of a certain column (a certain indicator) is less than or equal to 0, a "translation value" will be added to the data of this column at the same time [this value is the absolute value of the minimum value of a certain column of data + 0.01], In order to make the data all greater than 0, so as to meet the algorithm requirements.
(2) Multiple method
Screen out the data from 2018-2022 respectively, perform entropy value method 5 times, and then perform the operation of averaging the weight values obtained 5 times.
The SPSSAU screening operation is as follows:
After screening the year, the operation is the same as the one-time method, and the entropy value method is performed 5 times to obtain the weight value, and then the average value is taken.
Fourth, get the weight
(1) Calculation result of weight by one-time method
The "one-time method" performs the panel data entropy method to obtain the weight results as follows:
Use the entropy method to calculate the weight of a total of 5 items including NMMS_total liabilities. From the above table, it can be seen that the weight values of the 5 indicators are 18.58%, 11.93%, 19.45%, 21/93%, and 28.11%.
The SPSSAU output weight visualization results are as follows:
(2) Calculation results of multiple method weights
"Multiple times method" performs the panel data entropy method, and the weight summary results are as follows:
"Multiple times method" carries out the entropy value method, and the weight values of the five indicators are 37.54%, 28.74%, 29.97%, 24.07%, 18.46%, and 27.76%, respectively.
The comparison of the weight values obtained by the panel data entropy method by the two methods is shown in the table below. It can be seen that the two methods calculate the entropy value method of the panel data, and the obtained index weight values are close.
Tips: "Multi-time method" for panel data entropy analysis is feasible in principle. This approach is based on analysis considerations, taking into account the fluctuation of data in different years.
V. Summary
The entropy method for panel data is similar to the entropy method for ordinary data. First of all, it is necessary to unify the direction of the data, carry out positive processing on the positive indicators, and reverse the processing of the reverse indicators. If the data units are inconsistent, it is necessary to eliminate the influence of dimensions and standardize the data. However, after the data is dimensionally processed, negative values are likely to appear. The calculation process of the entropy method includes the operation of taking logarithms, so it is necessary to perform non-negative translation on the data to ensure that the analysis results can be obtained smoothly.
There are two methods to choose from the entropy method of panel data, which are "one-time method" and "multiple times method". The one-time method does not consider whether it is panel data, and it is enough to do one analysis like ordinary data; the multi-time method analyzes by year, calculates the weight of each year's indicators separately, and then takes the average. The index weight values obtained by the panel data entropy method by the two methods are close. The multi-time method takes into account the fluctuation difference of data in different years. The researchers of the two methods can choose to analyze the panel data entropy method.