【急】线性回归里的未标准化的β值和标准化的β值

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我想问各位大侠：
1. 线性回归里的未标准化的β值和标准化的β值的SE都一样的吗？
2. 我算标准化的β值和SE差不多相同，是什么原因呢？
3. 另外，像下图，我用标准化的β值±SE得到标化的β值的95%可信区间后发现P值有意义的但可信区间还包含0，是怎么回事呢？

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关键词：线性回归 标准化 是什么原因 可信区间 各位大侠

1. It is different, that is,
unstandardized coefficient(β): represents the effect of an independent variable on the dependent variable, net of the effects of the other independent variables

standardized coefficients or beta coefficients are the estimates resulting from an analysis performed on variables that have been standardized (mean=0, variance=1). This is usually done to answer the question of which of the independent variables have a greater effect on the dependent variable in a multiple regression analysis, when the variables are measured in different units of measurement (for example, income measured in dollars and family size measured in number of individuals). There is a big advantage when someone uses beta coefficients. They are directly comparable to one another, with the largest coefficient indicating which independent variable has the greatest influence on the dependent variable. On the other hand is difficult to interpret a linear model using beta coefficients

2. I believe that i gave you the answer.

3. When you say 95% CI = (mean-2se, mean+2se)

mssr 发表于 2011-9-17 01:13
1. It is different, that is,
unstandardized coefficient(β): represents the effect of an independe ...

Thank you very much! mssr. Your suggestions are really helpful!

One more question: is that means that if I use standardized coefficient, I cannot calculate the 95%CI for this coefficient, or according to 95%CI=mean-2se, mean+2se, the 95%CI for standardized coefficient would be (-2se, se), since mean=0?

Thanks!

No you must follow the formula:  StdBeta +/- 2*SE(StdBeta). In SPSS you cannot find, but in STATA you can use The simplest way is using the formula: SE(StdBeta_i) =[SD(Y)/SD(X_i)]*SE(beta_i) all of those numbers are available from regressoutput. Also, you could running a "regress" command using the standardized Xs variables in place of the original variables.

mssr 发表于 2011-9-20 03:02
No you must follow the formula:  StdBeta +/- 2*SE(StdBeta). In SPSS you cannot find, but in STATA yo ...

It's really really nice to meet you, mssr. Thank you very much!
I wondered if you could detail the process and the command how to calculate the StdBeta 95% CI by using STATA.
if:
Idependent variable: CRP
Dependent variable: TT
Adjusted variable: Age

Thank you very very much !

First of all the formula is [SD(x_i)/SD(y)]*SE(beta_i). I am really sorry.

The Stata command is:

1. regress TT CRP Age full beta

After that:
2. You will use the command "listcoef".The listcoef command gives more extensive output regarding standardized coefficients. It is not part of Stata, but you can download it over the internet like this

findit listcoef

and after installation you will see a more annotated output which gives you the same output with regress but with more four columns. (bStdX    bStdY   bStdXY      SDofX) You will notice in stata output that bStdXY is the same with Beta coefficient from previous output.

Oh, as I show in a forum there is another way which haw a small trick. Assuming that you are using SPSS, STATA or every other package and you will use multiple regression 2 times.

1. DV=TT, IV,s=CRP, Age and you take the unstandardized coefficients.

Now, the trick is that you will use Standardized dependent variables(DV) like as Independent Variables(IVs).

2. a. Use as DV the STD(TT) and IV,s STD(CRP) and STD(Age). For example in SPSS the path is:
Analyze -> Descriptives, moving the variables you want to standardize into the "Variables" window, and checking the box at the bottom that says "Save standardized values as variables."

After that you will run regression as before. In the second output you will notice that the column Unstandardised has same numbers as the column beta coefficient in first output. Of course you can choose to ask CI,s so you are OK.

mssr 发表于 2011-9-21 04:00
Oh, as I show in a forum there is another way which haw a small trick. Assuming that you are using S ...

Dear Professor:
Thank you very much! I have successfully calculated the SDBETA 95%CI with your and my senior colleague's help.
This will be a classical and substantial method to calculated SDBETA 95%CI，because some journals prefer 95% confidence intervals for the coefficient to SE. It will be perfect if you can answer me a last question.

Where's the difference when we use 95% or SE to interprete our result?

Best wishes!

PS: Sorry, when I repeat the linear regression in subgroup analyses, I found that although the standardized coefficients remained same whin each group, the unstadardized coefficients were different before and after by using Standardized variables, how to explain this fact and which BETA and 95%CI should I choose? Thank you!

In fact there is not difference and it depends from researcher how anyone would represent his statistical analysis. On the other hand in the literature tend to use 95% as a confidence interval, but we can use 99% or anything else as well.  For example if we see the CI formula about mean is: mean(X) +/-  se*zc where zc is the value of the normal distribution N(0,1). So if we want a 95% CI the precise formula is  mean(X) +/-  1,96* se  and because zc=1,96 ~= 2 that is we used to say mean(X) +/-  2* se,  but if we want a 99% CI the precise formula is  mean(X) +/-  2,58* se . So, many times the researchers tend to use in a column the standard errors and let the reader to decide what size of CI wants. You can see a normal table from any statistics book usually in appendix.  Moreover you can do a test. In spss you can use linear regression under Analyze-->Linear Regression(click the Statistics Button) and check confidence interval and change the by default value 95% to whatever you want.

Yes but as I show in the picture you didn't standardize the dependent variable as I have written in previous post .
PS. when use standardize variables constant has no meaning. So don't bother about constant.