How does factor analysis calculate weights?

One 、 Case description

Case background and research purpose

Study the weight of different dimensions of short video platform , The investigation collected 200 Data, of which 20 Items can be divided into brand activities , Brand spokesperson , Social responsibility , Five dimensions of brand sponsorship and purchase intention . The case data also includes basic individual characteristics such as gender 、 Age , Education , Monthly income, etc . And the viewing and consumption of short video platforms . The data sample is 200 individual .

Want to conduct factor analysis based on the data surveyed by the short video platform , The relationship between the judgment factor and the measurement item gets the corresponding dimension , For the secondary index, the entropy method is used to calculate the weight , The weight of primary indicators is calculated from the corresponding dimensions obtained by factor analysis , Final summary .

Two 、SPSSAU operation

Because the default dimension of the case is 5 So drag the analysis item to the right analysis box , The number of drop-down selection factors is 5. This case uses factor analysis to calculate the weight , So you don't need to check it “ Factor analysis ” And “ Comprehensive score ”.

SPSSAU

3、 ... and 、 Factor analysis results

1.KMO Value and Bartlete Spherical test

Using factor analysis for information enrichment research , First, analyze whether the research data is suitable for factor analysis , As can be seen from the table above ：KMO The value is 0.929, Greater than 0.6, Meet the prerequisite requirements of factor analysis , It means that the data can be used for factor analysis research . And data through Bartlett Sphericity test (p<0.05), It shows that the research data is suitable for factor analysis . Next, check whether the analysis item needs to be adjusted .

2. The relationship between the factor and the measured item

Factor analysis for factor concentration , It usually goes through multiple cycles , Delete unreasonable items , And repeat the cycle many times , Finally, a reasonable result . Generally, there are two kinds of situations , One is “ the wrong person ”, One is “ become entangled in ”, The details are as follows .

（1）“ the wrong person ”

In general , If 20 Item and 5 The corresponding relationship between the factors , Inconsistent with professional knowledge , For example, the first item should belong to the second factor but be divided under the first factor , In this case, it indicates that the item should be deleted , It appears ‘ the wrong person ’ The phenomenon . For example, in the case of “ Purchase intention 1” and “ Purchase intention 4”.

（2）“ become entangled in ”

except “ the wrong person ” The phenomenon , Sometimes there will be ‘ become entangled in ’ The phenomenon , For example, in the case of “ Brand sponsorship 4” Can be attributed to factors 2, It can also be attributed to factors 4, This is more normal （ Referred to as ‘ become entangled in ’）, It needs to be handled in combination with the actual situation , This item can be deleted , You can also not delete , At this time , Analysis is somewhat subjective .

Step1: The first analysis

This example contains 20 Analysis items , this 20 The analysis items are divided into 5 Dimensions , Therefore, you can take the initiative to tell SPSSAU, this 20 The term is five factors , otherwise SPSSAU Will automatically determine how many factors ( Usually, the automatic judgment of software is quite different from the actual situation , Therefore, it is recommended to actively set the number of factors ). Here's the picture ：

As can be seen from the above figure ：

Brand events 1-4 this 4 term , They all correspond to factors 1, The values of factor load coefficients are higher than 0.4, Illustrate this 4 Items should belong to the same dimension , That is, logically, brand activities 1-4 this 4 term , It didn't show up “ the wrong person ” The phenomenon .4 The values of analysis items belong to factors 1 None of the dimensions appear “ become entangled in ” The situation of .

Brand spokesperson 1-4 common 4 term , They all correspond to factors 1, But the brand spokesperson 3、 Brand spokesperson 4 At the same time, it belongs to the factor 3, Belong to “ become entangled in ”, Not to deal with temporarily .

“ Social responsibility 1-4” common 4 term , this 4 Each term corresponds to a factor 1 Or factor 3, this 3 Item does not appear ‘ the wrong person ’ problem , But there was “ become entangled in ”.

“ Brand sponsorship 1-4” common 4 term , They all correspond to factors 2,“ Brand sponsorship 4” It corresponds to the factor 2 And corresponding factor 4 There is “ become entangled in ”, Attention should be paid to .

“ Purchase intention 1-4” Four items in total , When they correspond to factors 4 be “ Purchase intention 1” appear “ the wrong person ” If the corresponding factor 5 be “ Purchase intention 4” appear “ the wrong person ”.

Summing up the above analysis, we can see ：“ Purchase intention 1” perhaps “ Purchase intention 4” These two items appear “ the wrong person ”, One of these two items should be deleted first ; And others appear “ become entangled in ” Phenomenal , Do not deal with （ Just pay attention ）. This time “ Purchase intention 1” Re analyze after deletion （ take “ Purchase intention 4” Deletion is also possible , It is up to the researcher to decide ）.

Step2: The second analysis

take “ Purchase intention 1” After this item is deleted , Conduct a second analysis . give the result as follows ：

It can be seen from the figure above “ Brand spokesperson 3”、“ Brand spokesperson 4” appear ‘ the wrong person ’ The phenomenon , Should delete , as well as “ Brand events 1-4”、“ Brand spokesperson 1-2” Etc ‘ become entangled in ’ The phenomenon , Not to deal with temporarily , But attention should be paid . Summing up ： Should be “ Brand spokesperson 3”、“ Brand spokesperson 4” Delete it first and then proceed to the... Again 3 dimensional analysis .

Step3: The third analysis

take “ Brand spokesperson 3”、“ Brand spokesperson 4” After deletion, the analysis results are as follows ：

It can be seen from the figure above

“ Brand spokesperson 1-2” Can also appear in factors 1 Sum factor 5 below , But considering the factors 5 Currently, only 2 term , Therefore, it means that it is acceptable , as well as “ Social responsibility 1-4” It's the same , Finally, find five factors , The correspondence between them and items is good . End of factor analysis .

3. The result after adjusting the factor

Because this case analysis focuses on the use of factor analysis to calculate weights, so for factor extraction 、 The results of information enrichment will be briefly described , If you want detailed analysis results, please log in SPSSAU Upload data for analysis .

4. Factor extraction and information enrichment

（1） Factor extraction

The above table is for factor extraction , And analyze the information extracted by factors , It can be seen from the above table that ： Factor analysis extracted 5 A factor , this 5 The variance interpretation rates after the rotation of the factors are 26.400%,21.703%,19.013%,15.359%,7.087%, The interpretation rate of cumulative variance after rotation is 89.563%. There is no fixed standard for the cumulative variance interpretation rate , Generally more than 60% All acceptable .

（2） Information enrichment

Load factor table after rotation

factor 1 Brand events ; factor 2 Brand sponsorship ; factor 3 Social responsibility ; factor 4 Purchase intention , factor 5 There is a higher load on , They mainly reflect the audience of the spokesperson used by a brand on the short video platform, which is the brand spokesperson . Use the variance interpretation rate after rotation to calculate the weight of five primary indicators ：

The weight of each dimension is normalized by the variance interpretation rate after rotation ： factor 1 The weight :0.264/0.896=0.295 factor 2 The weight ：0.217/0.896=0.242: factor 3 The weight ：0.190/0.896=0.212, factor 4 The weight 0.154/0.896=0.172, factor 5 The weight 0.071/0.896=0.079.

Here we are , End of factor analysis , The purpose of the above factor analysis is to judge the relationship between factors and measurement items , Repeat the analysis , Delete the analysis items that do not meet the analysis , Describe the corresponding five dimensions , Use the variance interpretation rate after rotation to calculate the weight of five primary indicators . Next use SPSSAU Calculate the weight of secondary indicators by entropy method, and then calculate the final weight .

Four 、 Calculation of secondary index weight

1. Secondary index weight results

Factor analysis will determine the final 17 Two secondary indicators are used SPSSAU Entropy method , because 17 Item is an index under five dimensions, so repeat the entropy analysis five times , Get the weight of the secondary indicators of brand activities as follows ：

Use entropy method to analyze brand activities 1 Wait a total 4 Item for weight calculation , As can be seen from the table above ： Brand events 1, Brand events 2, Brand events 3, Brand events 4 in total 4 term , Their weight values are 0.247, 0.266, 0.235, 0.252. And the weight of each item is relatively uniform , Both in 0.250 near .

The weight of brand sponsorship secondary indicators is as follows ：

Use entropy method to sponsor brands 1 Wait a total 4 Item for weight calculation , As can be seen from the table above ： Brand sponsorship 1, Brand sponsorship 2, Brand sponsorship 3, Brand sponsorship 4 in total 4 term , Their weight values are 0.225, 0.237, 0.271, 0.267. And the weight of each item is relatively uniform , Both in 0.250 near .

The weight of secondary indicators of social responsibility is as follows ：

The analysis results come from SPSSAU

Use entropy method for social responsibility 1 Wait a total 4 Item for weight calculation , As can be seen from the table above ： Social responsibility 1, Social responsibility 2, Social responsibility 3, Social responsibility 4 in total 4 term , Their weight values are 0.254, 0.256, 0.224, 0.265. And the weight of each item is relatively uniform , Both in 0.250 near .

The weight of the brand spokesperson's secondary indicators is as follows ：

Use entropy method to analyze brand spokesperson 1 Wait a total 2 Item for weight calculation , As can be seen from the table above ： Brand spokesperson 1, Brand spokesperson 2 in total 2 term , Their weight values are 0.490, 0.510. And the weight of each item is relatively uniform , Both in 0.500 near .

The weights of secondary indicators of purchase intention are as follows ：

The analysis results come from SPSSAU

Use the entropy method to measure the purchase intention 2 Wait a total 3 Item for weight calculation , As can be seen from the table above ： Purchase intention 2, Purchase intention 3, Purchase intention 4 in total 3 term , Their weight values are 0.327, 0.340, 0.332. And the weight of each item is relatively uniform , Both in 0.333 near .

To sum up, you can get brand sponsorship 、 Social responsibility 、 Brand spokesperson 、 The weights of brand activities and purchase intention are 0.242、0.212、0.079、0.295 as well as 0.172. Sort out the primary and secondary indicators as follows and calculate the corresponding final weight .

2. Final weight result

such as , The weights of the first level indicators are calculated as 0.242、0.212、0.079、0.295 as well as 0.172. Second level indicator purchase intention 2 The weight of 0.327, Then purchase intention 2 The final weight value is 0.172*0.327=0.06. According to the weight results, it can be found that the weight distribution of each primary index is uniform , For platform short videos, you can also pay attention to users “ Brand events ”.

5、 ... and 、 summary

This case mainly uses SPSSAU Analyze and calculate the weight , The methods used include the combination of factor analysis and entropy method , Because this case uses factor analysis to calculate the weight , So you don't need to check it “ Factor analysis ” And “ Comprehensive score ”. Adjust the corresponding analysis items through the relationship between factors and measurement items , After adjustment, the result of factor analysis , The results of irrelevant weights will not be repeated , Finally, the weight of analysis items and primary indicators under the corresponding dimensions is obtained , Entropy method is used to calculate the weight of secondary indicators , Because of the five dimensions obtained from the analysis, the entropy method analysis is repeated five times , The final weight of each item is obtained by using the weight results of factor analysis and entropy method .