Adjustment regression

This blog post mainly talks about the concept of adjustment regression, its operation process and some precautions . For the conceptual part of this blog post, you can directly read Chapter 12 of "Quantitative Research and Statistical Analysis: SPSS (PASW) Data Analysis Example Analysis" by Mr. Qiu Haozheng, so you don’t have to read what I wrote, and then the precautions in the blog post or It is worth seeing the summary of the operation.

0. Some basic concepts of regression

I really have a lot of new understanding after reading this book. Thanks, I will put the concepts in the book directly below.

1. Regulating regression concept

We all know that independent variables in regression can be divided into many types: explanatory variables, control variables, regulatory variables, and so on. Regulated regression is also a regression with adjustment variables. Specifically, if Y is the dependent variable, X is the explanatory variable, and Z is the moderating variable, then the adjusted regression is:
$$Y=a_1+a_2\ast X+a_3\ast WITH+a_4\ast XZ+\eta \; You$$
may be unfamiliar with the term “regulation regression”, but you can understand the above formula at once, that is, regression with interaction terms. Its actual meaning is that under different Z levels, the relationship between Y and X will change. Next, I will borrow the pictures in the book to explain it very clearly. The c adjustment model is the adjustment regression, which means that Z will affect the relationship between X and Y.

3. Operation process

1. Analyze the problem and determine the explained variables, explanatory variables, control variables, and adjustment variables.
2. It needs to be divided into categorical variables and continuous variables according to the moderating variables (explanatory variables are exactly the same when they are categorical variables or continuous variables, because the moderating variables and explanatory variables are mutual, different perspectives are different explanatory variables and moderating variables.) Two cases are discussed: Case 1: The explanatory variable is continuous, and the moderating variable is continuous: the explanatory variable is deflated (centralization), the moderating variable is deflated (centralized), and the explanatory variable after deflation is flat The subtracted moderating variables are multiplied to obtain the interaction term, and then the obtained interaction term is flattened (centralized) to obtain the flattened interaction term, and the dependent variable does not need to be processed. Case 2: The explanatory variable is continuous, and the moderating variable is a categorical variable: the explanatory variable is subtracted (centralized), the moderating variable is not processed, and the subtracted explanatory variable is multiplied by the moderating variable to obtain the interaction term. Further deflate.
3. Hierarchical regression is performed. The first-level regression includes deflated explanatory variables, the second-level regression includes (deflated) adjustment variables, and the third-level regression includes (deflated) interaction terms. Remember to output the changed R_square.
4. Interpret the model, and if the interaction term is significant, perform a simple effect test. It also needs to be divided into continuous variables and categorical variables. Case 1: The explanatory variable is continuous, and the moderating variable is continuous: Take 3 values ​​for the moderating variable: average value-standard deviation, average value, average value + standard deviation, respectively The regression equation of the adjusted variable under these three values ​​can further explain the relationship between the dependent variable and the independent variable at different levels of the adjusted variable. Case 2: The explanatory variable is continuous, and the regulatory variable is a categorical variable: regression equations are obtained at different regulatory variable levels, so the relationship between the dependent variable and the independent variable can be analyzed at different regulatory variable levels.

4. Matters needing attention

The main thing is to pay attention to the deflation, because the correlation between the interaction term and the explanatory variable and the moderating variable must be very high. If there is no deflation, there will be multicollinearity problems. The deflation method can greatly reduce them. The correlation between. And it should be noted that when both the explanatory variable and the moderating variable are continuous variables, a deflation is required after the interaction term is obtained. This is mainly for the intercept term of the final regression equation to be meaningful, that is, the intercept term is the average value of Y. In fact, we generally don't pay much attention to the average value of Y, so the deflation of the last interaction item does not have a big impact, but the book says so, it is recommended to deflate the interaction item. Then note that the dependent variable does not need to be deflated. When the moderating variable is a categorical variable, the explanatory variable must be deflated, but the categorical variable and the interaction term do not need to be deflated, which means that the continuous variable must be deflated, and the categorical variable is unnecessary. In addition, the explanatory variable may be categorical, and the moderating variable is continuous. In this case, the explanatory variable is continuous, and the moderating variable is categorical. It is the same, because as I said earlier, the explanatory variable and the moderating variable are mutual. It's just looking at the problem from a different angle. Finally, if both the explanatory variable and the moderating variable are classified, it would be fine without deflation, but this situation is not mentioned in the book, and there is no example, but according to my understanding, it should be like this.
Regarding the operation method of spss, you can read this book by yourself. The operation process is shown in the book, but I think the operation is not difficult, so I won't repeat it here.

references

"Quantitative Research and Statistical Analysis: Analysis of SPSS (PASW) Data Analysis Example" by Qiu Haozheng

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Afterwards, the part of returning to the mediation effect has basically come to an end.