Normalization of variable does not give 0 and 1

[Andreas Grytten]

Im comparing the coefficients of two variables with different units. I want both to be normalized so that the coefficients are easy to compare, cause thats what I have to do in the text I submit.
One of them get the values 0 and 1 when normalized, but the other variable (which measures subjective social status) gives values min -.2994705 and max .1241556. Is that at problem?

[George Ford]

is it continuous?

[Andreas Grytten]

is it continuous?

No, its discrete. The variable ranges from 1-11, where 1 is the lowest subjective status and 11 the highest. The other variable that is normalized successfully is a composite variable measuring objective social status, made from standardizing and normalizing three components (education, job prestige and income) before combining them together to make the variable "objective social status". This variable is also made from two discrete variables (job prestige and education) but income is continous, so maybe thats why it worked. I also used rowmean to combine the three of them. I also had to standardize my subjective status-variable before normalizing it, othwerwise all observations went missing.

Maybe I should not normalize my subjective status variable, but the goal of the text is to compare how much effect objective and subjective status has on altruistic sharing, so it would be practical to have them both normalized for easier comparison of effects.

[Nick Cox]

I can easily follow what you've done. Please define normalize and show the Stata commands you used.

[Nick Cox]

Sorry: can should be can't.

[Andreas Grytten]

Sorry: can should be can't.

I have now managed to normalize the variable for subjective status. Sorry for not being precise in my description: I made 0-1 normalized variables.

I forgot to use summarize in the step before normalizing

egen subjektivstatus1 = std(QID9_1 - 1)
su subjektivstatus1
gen subjektivstatus = (subjektivstatus1-r(min))/(r(max)-r(min))
tab subjektivstatus

Im not sure if it was necessary to standardize the variable before normalizing it, but it seems like it worked in the end, considering the variable now has min value of 0 and max 1.

The two pictures show two regression models, the goal with both of them is to measure altruism, based on how much of the money the were willing to share in an experiment. In the first model objective status is used as explanatory variable, and in the second one, subjective status is used. "prososialitet" is the dependent variable, measuring altruism (percent of 15 dollars respondents are willing to share with someone the dont know".

The goal is to find out if there is a difference between how much people share based on their social status. I want to compare the subjective status dimension and the objective status dimension. Since both are min/max normalized, the coefficients for status is the difference of altruism between the lowest status individuals and the highest status individuals? If I understand it correctly, high status individuals (both objective status and subjective status) share more of the sum of money in the experiment? Given the positive coefficients? And subjective status has a larger difference between low status/high status regarding altruism, with a coefficient of 17 vs 7 for objective status? All the other variables are control variables and written in norwegian. Thanks for helping me!

[Maarten Buis]

Standardization step was not necessary.

However, be careful. What you did rests on the assumption that answering the minimum value on the objective social status is equivalent to answering the minimum value on subjective social status, and the same for the maximum value. If the objective status is something like ISEI and the subjective status something like lower, middle higher, then that is not a realistic assumption, and the two variables are not comparable even if you normalized them. Also, is status continuous or categorical? Also, consider adding both to the model: what is the effect of the subjective believe that you belong to the middle class net of your objective class characteristics.

[Nick Cox]

Thanks for the further details. DIfferent groups of researchers have different cultures in data analysis. I work most with environmental data in which often variables have conventional units, elevation or altitude in m, temperature in deg C, rainfall in mm, and so on. I never adjust those scales except by multiples of 10 if some numbers are very much larger than others. I want to interpret coefficient estimates in terms of the units of measurement and I am happy to take t or z statistics as indicating (with many reservations) the relative importance of each predictor in a regression-type model. So, I never standardize or normalize in your sense, but you've made what you're doing a bit clearer for people who do do that and may wish to comment.

Beyond that, I note R-square of 3% which for my line of work would be a big disappointment, but your field is quite different.

[Maarten Buis]

Beyond that, I note R-square of 3% which for my line of work would be a big disappointment, but your field is quite different.

In general, that is not too unexpected; humans are weird.

[Andreas Grytten]

Standardization step was not necessary.

However, be careful. What you did rests on the assumption that answering the minimum value on the objective social status is equivalent to answering the minimum value on subjective social status, and the same for the maximum value. If the objective status is something like ISEI and the subjective status something like lower, middle higher, then that is not a realistic assumption, and the two variables are not comparable even if you normalized them. Also, is status continuous or categorical? Also, consider adding both to the model: what is the effect of the subjective believe that you belong to the middle class net of your objective class characteristics.

Objective status is composed of ISEI, education and income. Subjective status is composed on the basis of MacArthur scale from 1-11 where respondents are asked to place themselves on the social status ladder in the society they live in. I also have a model with both objective status and subjective status in the same regression model, and that leads to objective status having a p-value of 0,8 with all the controls, and 0,3 by only controlling for gender and age. It looks like subjective status maybe functions like a mediator between objective status and subjetive status. Individuals internalize their objective status and the status becomes subjective, and altruism(coded as prososialitet i the regression) is then affected through this mediation path.

So I ran a mediation model with subjective status as mediatior between objective status(x) and altruism(y). The results show that about 71 % of the effect of objektivstatus on altruism is mediated by subjektivstatus. I interpret this as subjective status is an important part of the social status and altruism nexus, and that subjective status plays a bigger role in determening altruistic sharing in the Money Dictator Game. I will put in a screenshot of the mediation. Also: It is not possible to use "bysort country" in the medsem command, so I cant distinguish between the swedish and american respondents..and I also cant find a way to include control variables in the mediation analysis. I have red a paper on the medsem package for mediation, and also watched some youtube tutorials, but Im not able to include control variables. But maybe the point of mediation analysis is to only investigate the mediation effect, and not coefficients, so that controls should not be included in the first place?

[Maarten Buis]

Just to make your life a little bit harder (sorry):

ISEI is already based on income and education: It scales occupation such that the indirect of education through occupation on income is maximized. So combining ISEI again with education and income is at least a little weird.

More importantly, what is this "objective status" supposed to measure and how would that influence altruistic behavior? I suppose you imagine it to be some measure of generalized privilege. But does that even exist, and if it does, is it really one dimensional as your measure suggests? For example, we can think of extremes like someone like Trump who is rich, but has zero cultural capital (and is proud of it) and compare him with a "struggling artist" who is poor but has a lot more cultural capital. How would generalized privilege influence altruistic behavior? If it is just material resource available to an individual, then we can have two competing theories: The rich spent more on altruistic causes because they can afford it or the poor spent (relatively) more on altruistic causes because they can better relate to other poor people. Interesting special cases in that context are people who were poor and became rich and people who where rich and became poor. If you have income in your dataset, then you do not want to muddle that variable with things like education and occupation when testing that theory. If you are looking for a more cultural explanation then you may posit that there may be a "noblesse oblige" attitude among the higher social classes. Now you are entering Marxist theory so you want to look at occupation and nothing else. But I cannot think of a theory that would involve generalized privilege.