topic Re: a question regarding statistics in SAS Data Science

a question regarding statistics

Ahmad — Sat, 30 Mar 2013 01:17:04 GMT

hi i have estimated regression using 'Proc REg' with' by' variable.

now i regression result for all the 'by variable'

i want to average the slope coefficient. well that is easy . but what about to the t statistic? can i simply average it too? and how to interpret it?

Thanks in advance

Re: a question regarding statistics

Reeza — Sat, 30 Mar 2013 01:53:38 GMT

No, you can't just average the t-stat or p-value.

What are you actually trying to calculate?

Re: a question regarding statistics

Ahmad — Sat, 30 Mar 2013 03:21:02 GMT

ok thanks for the reply , here is what i am trying to calculate.

i have weekly liquidity data for 500 stock over 7 years.

i am estimating an equation, which is something like this

Liq= a+ b1x + b2z+ b3d........+bnZ +e

now i have estimated this equation using proc reg .

with stockname as my by variable. so i have estimated this equation 500 times (number of stocks)

for reporting purpose i need to calculate the cross sectional average of coefficients (e.g average 500 b1). How do i report the t statistics for these averaged coefficients??? .

Re: a question regarding statistics

Ahmad — Sat, 30 Mar 2013 17:23:58 GMT

help please once again

Re: a question regarding statistics

PGStats — Sat, 30 Mar 2013 19:35:40 GMT

I agree with Reeza that averaging your coefficients is NOT the way to go. Instead, you should estimate single slope coefficients from all your stocks taken together. Drop the BY clause, switch from REG to GLM and use something like:

proc glm data=myData;

class stockName;

model liq = stockName x z d / solution;

run;

This will estimate a separate intercept for each stock and single slopes (with T statistics) for all your parameters (x, z, d, etc)

Re: a question regarding statistics

Reeza — Sat, 30 Mar 2013 20:10:54 GMT

If you have time series data, data over 7 years, then its likely you should be doing some sort of time series analysis rather than proc reg or GLM in my opinion.

Re: a question regarding statistics

Ahmad — Sat, 30 Mar 2013 21:20:40 GMT

but this procedure has been used in alot of recent papers in top journals, and they just average out the slope coefficients, however how they go about tstatistics, i am not sure and i cant understand

Re: a question regarding statistics

Reeza — Sat, 30 Mar 2013 22:34:00 GMT

That explains why the market crashed

Re: a question regarding statistics

Ahmad — Sun, 31 Mar 2013 01:26:35 GMT

haha nice one :smileysilly: but you know the problem is not with estimtaion, because this estimation becuase this is just an intermediate estimation before the real model, however we cannot report the result of 500 regression, so just for reporting purpose this has to be done, and i just cant figure out how they have done or how to report, if you want i can send you a link of the orignal paper, sorry to bother but any help wpold be really appreciated

Re: a question regarding statistics

AncaTilea — Sun, 31 Mar 2013 02:05:05 GMT

Ahmad,

It could help to see the paper you are referring to.

Maybe there is some misunderstanding on the methodology used?

Re: a question regarding statistics

PGStats — Sun, 31 Mar 2013 02:20:24 GMT

Maybe all you need is some descriptive statistics for a population of 500 regression parameters. Maybe, you could do something simple as in the folowing example:

proc sort data=sashelp.cars out=cars; by origin; run;

proc reg data=cars outest=carsEst noprint;
by origin;
model horsepower = engineSize Weight;
run;

proc summary data=carsEst noprint;
var engineSize Weight;
output out=carsMeanEst mean= std= probt= / autoname autolabel;
run;

proc print data=carsMeanEst; run;

PS. Just don't associate my name to that idea! - PG

Re: a question regarding statistics

Ahmad — Sun, 31 Mar 2013 02:48:38 GMT

here let me attach the paper , see table2 on page 266, the author has just calculated equally weighted average of the coefficients

Re: a question regarding statistics

Ahmad — Sun, 31 Mar 2013 02:50:33 GMT

and here is the other paper, to which the author of the previous paper is referring to

Re: a question regarding statistics

Reeza — Sun, 31 Mar 2013 17:36:58 GMT

On pg 266, that is time series analysis, not just regression analysis. Because there is seasonal adjustment and time adjustments.

You can implement a similar model in proc reg, but have to make sure your have the appropriate terms in the model as well.

Re: a question regarding statistics

Ahmad — Sun, 31 Mar 2013 17:43:08 GMT

yes reeza i have all the appropriate terms, i.e lags and everything, but do you know how the author has summarized the results in table2, specially regarding the tstatistic, as he has averaged the coefficients cross sectionally, but how do i report t statistics??

Re: a question regarding statistics

Reeza — Mon, 01 Apr 2013 14:55:47 GMT

I'm not sure, mostly because I don't want to read the paper thoroughly.

I would suggest contacting the authors directly. The version you attached doesn't have the author contacts, but usually when I've had articles published the author contacts are included, as well as the institutions.

Re: a question regarding statistics

adjgiulio — Mon, 01 Apr 2013 16:52:41 GMT

I'm not sure how the author came up with the average t-statistic. I agree that it is a bad practice averaging t-statistics. If you have the opportunity to recommend a different solution, I would probably go for something like "% of regressions with a significan p-value". It's a way to say, for each independent variable, of the n "by groups", x% had a significan p-value.

Re: a question regarding statistics

Ahmad — Wed, 03 Apr 2013 01:16:01 GMT

i have found this explanation so far can you please guide me if you understand what the author has done??

"The t-statistics associated with the mean coefficients in Table 2 have been adjusted for cross-equation correlations. We extend the correction in standard errors proposed in Chordia et al. (2000) by allowing the variance and pairwise covariances between coefficient estimates to vary across securities. The variance of each estimated coefficientβ_iis obtained from stock i’s liquidity-return regression in (2). The empirical correlation between the regression residuals for stocks i and j is used to estimate the pairwise correlation between the coefficients{β_iandβ_j}. Hence, the standard error of the mean estimated coefficient is ...

please find the attached JPEG file it is just snapshot of the equation used, dont know how to enter an equation here. thanks

Re: a question regarding statistics

SteveDenham — Wed, 03 Apr 2013 14:38:07 GMT

The equation given is a pretty standard summation version of the standard error of a difference between two correlated variables. Plug in the necessary variables, get the std error, and calculate the t value as the difference between the estimates divided by the standard error.

Steve Denham

Re: a question regarding statistics

Ahmad — Thu, 04 Apr 2013 02:44:43 GMT

thanks , but the problem is i have hundreds of b's which are the necessary variables. they sat that they have calculated the pairwise correlation from the rsu=iduals of the orignal regressions, so how to calculate the pairwise correlation of residuals of these 100 equations???