關(guān)于調(diào)節(jié)效應(yīng)和中介效應(yīng)里變量中心化的問題，急。

xuezhe116 發(fā)表于 2013-6-15 15:07
正確。溫忠麟《調(diào)節(jié)效應(yīng)和中介效應(yīng)》P84、P96

我能問個問題嗎？“如果調(diào)節(jié)變量和自變量都是通過因子分析得到的以0為中心標準化變量，這樣的話，出現(xiàn)了不少負數(shù)，那么負數(shù)乘以負數(shù)就是正數(shù)，與實際矛盾，因此在進行調(diào)節(jié)研究之前，將兩個變量移動為以4為中心的變量；因為題項是五個選項，4表示中立”這么理解對嗎？

http://www.ats.ucla.edu/stat/sas/faq/centering_variables.htm

http://stats.stackexchange.com/q ... uld-you-standardize

http://www.theanalysisfactor.com ... able-in-regression/

When NOT to Center a Predictor Variable in Regression

KAREN

There are two reasons to center predictor variables in any time of regression analysis–linear, logistic, multilevel, etc.

• To lessen the correlation between a multiplicative term (interaction or polynomial term) and its component variables (the ones that were multiplied).
• To make interpretation of parameter estimates easier.
  

I was recently asked when is centering NOT a good idea?

Well, basically when it doesn’t help.

For reason #1, it will only help if you have multiplicative terms in a model.  If you don’t have any multiplicative terms–no interactions or polynomials–centering isn’t going to help.For reason #2, centering especially helps interpretation of parameter estimates (coefficients) when:

• You have an interaction in the model
• Particularly if that interaction includes a continuous and a dummy coded categorical variable and
• If the continuous variable does not contain a meaningful value of 0;
• even if 0 is a real value, if there is another more meaningful value, such as a threshhold point.  (For example, if you’re doing a study on the amount of time parents work, with a predictor of Age of Youngest Child, an Age of 0 is meaningful and will be in the data set, but centering at 5, when kids enter school, might be more meaningful).
  

So when NOT to center:

1. If all continuous predictors have a meaningful value of 0.
2. If you have no interaction terms involving that predictor.
3. And if there are no values that are particularly meaningful.

Should You Always Center a Predictor on the Mean?

KAREN GRACE-MARTIN

Centering predictor variables is one of those simple but extremely useful practices that is easily overlooked.

It’s almost too simple.

Centering simply means subtracting a constant from every value of a variable.  What it does is redefine the 0 point for that predictor to be whatever value you subtracted.  It shifts the scale over, but retains the units.

The effect is that the slope between that predictor and the response variable doesn’t change at all.  But the interpretation of the intercept does.

The intercept is just the mean of the response when all predictors = 0.  So when 0 is out of the range of data, that value  is meaningless.  But when you center X so that a value within the dataset becomes 0, the intercept becomes the mean of Y at the value you centered on.

What’s the point?  Who cares about interpreting the intercept?

It’s true.  In many models, you’re not really interested in the intercept.  In those models, there isn’t really a point, so don’t worry about it.

But, and there’s always a but, in many models interpreting the intercept becomes really, really important.  So whether and where you center becomes important too.

A few examples include models with a dummy-coded predictor, models with a polynomial (curvature) term, and random slope models.

Let’s look more closely at one of these examples.

In models with a dummy-coded predictor, the intercept is the mean of Y for the reference category—the category numbered 0.  If there’s also a continuous predictor in the model, X2, that intercept is the mean of Y for the reference category only when X2=0.

If 0 is a meaningful value for X2 and within the data set, then there’s no reason to center.  But if neither is true, centering will help you interpret the intercept.

For example, let’s say you’re doing a study on language development in infants.  X1, the dummy-coded categorical predictor, is whether the child is bilingual (X1=1) or monolingual (X1=0).  X2 is the age in months when the child spoke their first word, and Y is the number of words in their vocabulary for their primary language at 24 months.

If we don’t center X2, the intercept in this model will be the mean number of words in the vocabulary of monolingual children who uttered their first word at birth (X2=0).

And since infants never speak at birth, it’s meaningless.

A better approach is to center age at some value that is actually in the range of the data. One option, often a good one, is to use the mean age of first spoken word of all children in the data set.

This would make the intercept the mean number of words in the vocabulary of monolingual children for those children who uttered their first word at the mean age that all children uttered their first word.

One problem is that the mean age at which infants utter their first word may differ from one sample to another. This means you’re not always evaluating that mean that the exact same age.  It’s not comparable across samples.

So another option is to choose a meaningful value of age that is within the values in the data set. One example may be at 12 months.

Under this option the interpretation of the intercept is the mean number of words in the vocabulary of monolingual children for those children who uttered their first word at 12 months.

The exact value you center on doesn’t matter as long it’s meaningful, holds the same meaning across samples,  and within the range of data.  You may find that choosing the lowest value or the highest value of age is the best option. It’s up to you to decide the age at which it’s most meaningful to interpret the intercept

zhongmin5788 發(fā)表于 2012-4-30 02:38
根據(jù)我對香港教授kenneth的中人網(wǎng)上與中介、調(diào)節(jié)有關(guān)的問題的匯總：
調(diào)節(jié)：只有自變量、調(diào)節(jié)變量須中心化， ...

為什么調(diào)節(jié)分析的時候，因變量不用標準化呢？因變量問項的數(shù)量級也是不同的，如此一來，如何匯總因變量呢？而且就算是因子分析計算得分系數(shù)，也是在標準化之后進行的分析。麻煩幫忙解答一下，非常感謝!

zhongmin5788 發(fā)表于 2012-4-30 02:38
根據(jù)我對香港教授kenneth的中人網(wǎng)上與中介、調(diào)節(jié)有關(guān)的問題的匯總：
調(diào)節(jié)：只有自變量、調(diào)節(jié)變量須中心化， ...

多謝！

xuezhe116 發(fā)表于 2013-6-15 15:07
正確。溫忠麟《調(diào)節(jié)效應(yīng)和中介效應(yīng)》P84、P96

贊   是的

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