standard errors for combined coefficients

[Maguin, Eugene]

All,

Having done a regression with an interaction term, I'd like to provide an estimate of the sum of main effects plus interactions for the groups represented by the main effects and interaction. I figure I can sum products of coefficients and values. But what about the standard error for the result? What is the formula? Could it be sqrt(var(B1)+var(B2)+2*cov(B1,B2))?

Thanks, Gene Maguin

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

[Maguin, Eugene]

Sure. Suppose x1 and x2 and their interaction, x12, are ivs. Let x1 and x2 be dichotomous contrast variables (0,1 coding). Four groups are defined.
B(x1) = -0.24 (.044), B(x2) = 0.09 (.005), B(x12) = -0.23 (.10).

Effect = B(x1)*x1 + B(x2)*x2 + B(x12)*x12.
SE(effect) = sqrt(.044**2 + .005**2 + 2*.10**2).

Gene Maguin




-----Original Message-----
From: Santosh Pande [mailto:[hidden email]]
Sent: Tuesday, January 08, 2013 9:41 AM
To: Maguin, Eugene
Subject: RE: standard errors for combined coefficients



Hi Eugene,

I have read your email with interest and am sending this request to you elaborate what you mean by "I figure I can sum products of coefficients and values".

Could you please elaborate with an example?

Much appreciated.

Thanks & Regards

Santosh Pande
Mobile No.: [phone]
-----------------------------------------------
view my research on my SSRN Author page:
http://ssrn.com/author=1714442



-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Maguin, Eugene
Sent: Tuesday, January 08, 2013 7:45 PM
To: [hidden email]
Subject: standard errors for combined coefficients

All,

Having done a regression with an interaction term, I'd like to provide an estimate of the sum of main effects plus interactions for the groups represented by the main effects and interaction. I figure I can sum products of coefficients and values. But what about the standard error for the result? What is the formula? Could it be sqrt(var(B1)+var(B2)+2*cov(B1,B2))?

Thanks, Gene Maguin

=====================
To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD

-**************Nihilent***************
" *** All information contained in this communication is confidential, proprietary, privileged and is intended for the addressees only. If youhave received this E-mail in error please notify mail administrator by telephone on [phone] or E-mail the sender by replying to this message, and then delete this E-mail and other copies of it from your computer system.
Any unauthorized dissemination,publication, transfer or use of the contents of this communication, with or without modifications is punishable under the relevant law.

Nihilent has scanned this mail with current virus checking technologies. However, Nihilent makes no representations or warranties to the effect that this communication is virus-free.

Nihilent reserves the right to monitor all E-mail communications through its Corporate Network. *** "

*************************************************************************-

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

[Bruce Weaver]

Hi Gene.  The variance of a sum is the sum of all the terms in the corresponding covariance matrix.  E.g.,

   http://en.wikipedia.org/wiki/Variance#Sum_of_correlated_variables

So your formula gives the SE of (B1+B2).  But it sounds like you want SE(B1+B2+B3), where B3 is the coefficient for the interaction.  

VAR(B1+B2+B3) = the sum of the terms in a 3x3 covariance matrix, as follows:

11  12  13
21  22  23
31  32  33

= Var(B1) + Var(B2) + Var(B3) + 2*COV(1,2) + 2*COV(1,3) + 2*COV(2,3)

And the SE = the square root of that variance.

HTH.

Maguin, Eugene wrote

All,

Having done a regression with an interaction term, I'd like to provide an estimate of the sum of main effects plus interactions for the groups represented by the main effects and interaction. I figure I can sum products of coefficients and values. But what about the standard error for the result? What is the formula? Could it be sqrt(var(B1)+var(B2)+2*cov(B1,B2))?

Thanks, Gene Maguin

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

[Maguin, Eugene]

Thank you, Bruce. That's right, I do have three variances to sum.  Gene

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Bruce Weaver
Sent: Tuesday, January 08, 2013 10:14 AM
To: [hidden email]
Subject: Re: standard errors for combined coefficients

Hi Gene.  The variance of a sum is the sum of all the terms in the corresponding covariance matrix.  E.g.,

   http://en.wikipedia.org/wiki/Variance#Sum_of_correlated_variables

So your formula gives the SE of (B1+B2).  But it sounds like you want SE(B1+B2+B3), where B3 is the coefficient for the interaction.

VAR(B1+B2+B3) = the sum of the terms in a 3x3 covariance matrix, as follows:

11  12  13
21  22  23
31  32  33

= Var(B1) + Var(B2) + Var(B3) + 2*COV(1,2) + 2*COV(1,3) + 2*COV(2,3)

And the SE = the square root of that variance.

HTH.



Maguin, Eugene wrote

> All,
>
> Having done a regression with an interaction term, I'd like to provide
> an estimate of the sum of main effects plus interactions for the
> groups represented by the main effects and interaction. I figure I can
> sum products of coefficients and values. But what about the standard
> error for the result? What is the formula? Could it be
> sqrt(var(B1)+var(B2)+2*cov(B1,B2))?
>
> Thanks, Gene Maguin
>
> =====================
> To manage your subscription to SPSSX-L, send a message to

> LISTSERV@.UGA

>  (not to SPSSX-L), with no body text except the command. To leave the
> list, send the command SIGNOFF SPSSX-L For a list of commands to
> manage subscriptions, send the command INFO REFCARD





-----
--
Bruce Weaver
[hidden email]
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

--
View this message in context: http://spssx-discussion.1045642.n5.nabble.com/standard-errors-for-combined-coefficients-tp5717270p5717272.html
Sent from the SPSSX Discussion mailing list archive at Nabble.com.

=====================
To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

[David Marso]

In general that can be expressed in a matrix quadratic form.
given L=c'B where c' is a vector of coefficients in this case {1,1,1}
Var(L)= c'Sc (S is the Covariance matrix of the B's).

Say you wanted B1+B2-B3, then c'={1,1,-1}
you would end up with
{1,1,-1} {s11, s12, s13;     {1;
               s21,s22,s23;        1;
               s31,s32,s33}      -1}

={s11+s21-S31,s12+s22-s32 ,s13+s23-s33} * {1;1;-1}
={s11+s21-S31 + s12+s22-s32 -s13-s23+s33}
= s11+s22+s33 + 2*(s12 - s13 - s23)

Maguin, Eugene wrote

Thank you, Bruce. That's right, I do have three variances to sum.  Gene

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Bruce Weaver
Sent: Tuesday, January 08, 2013 10:14 AM
To: [hidden email]
Subject: Re: standard errors for combined coefficients

Hi Gene.  The variance of a sum is the sum of all the terms in the corresponding covariance matrix.  E.g.,

   http://en.wikipedia.org/wiki/Variance#Sum_of_correlated_variables

So your formula gives the SE of (B1+B2).  But it sounds like you want SE(B1+B2+B3), where B3 is the coefficient for the interaction.

VAR(B1+B2+B3) = the sum of the terms in a 3x3 covariance matrix, as follows:

11  12  13
21  22  23
31  32  33

= Var(B1) + Var(B2) + Var(B3) + 2*COV(1,2) + 2*COV(1,3) + 2*COV(2,3)

And the SE = the square root of that variance.

HTH.



Maguin, Eugene wrote
> All,
>
> Having done a regression with an interaction term, I'd like to provide
> an estimate of the sum of main effects plus interactions for the
> groups represented by the main effects and interaction. I figure I can
> sum products of coefficients and values. But what about the standard
> error for the result? What is the formula? Could it be
> sqrt(var(B1)+var(B2)+2*cov(B1,B2))?
>
> Thanks, Gene Maguin
>
> =====================
> To manage your subscription to SPSSX-L, send a message to

> LISTSERV@.UGA

>  (not to SPSSX-L), with no body text except the command. To leave the
> list, send the command SIGNOFF SPSSX-L For a list of commands to
> manage subscriptions, send the command INFO REFCARD





-----
--
Bruce Weaver
[hidden email]
http://sites.google.com/a/lakeheadu.ca/bweaver/

"When all else fails, RTFM."

NOTE: My Hotmail account is not monitored regularly.
To send me an e-mail, please use the address shown above.

--
View this message in context: http://spssx-discussion.1045642.n5.nabble.com/standard-errors-for-combined-coefficients-tp5717270p5717272.html
Sent from the SPSSX Discussion mailing list archive at Nabble.com.

=====================
To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD