Problem specifying MIXED model with heterogeneous variances
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Problem specifying MIXED model with heterogeneous variances
 
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I apologize up front for the length & complexity of this post. Anyone who decides to read it seriously is advised to have a cup (or maybe a pot) of strong coffee at the ready! ;-)
I've been reading this article by Hoffman & Rovine (2007), and looking at the SPSS syntax they provide here. Table 3 in the article shows 3 models for analysis of data with repeated measures: 2A - Main effects only with homogeneous variances 2B - Main effects only with heterogeneous variances 3B - Main effects & selected interactions with heterogeneous variances The SPSS syntax for these models is found in file MLM_AppendixA.sps (which is in the .zip from the link given above). Before anyone freaks out, let me point out that the data management steps in that syntax file could have been done a lot more efficiently. ;-) But that's not what I'm asking about. Here is the MIXED command they used to run model 2A above (note that they had command terminators on both /RANDOM sub-commands, and I had to remove the first one to get the model to run): MIXED lg_rt BY ID Item WITH c_mean c_sal oldage yrs65 /FIXED = c_mean c_sal oldage yrs65 /METHOD = ML /PRINT = SOLUTION TESTCOV R /RANDOM = INTERCEPT | SUBJECT(Item) COVTYPE(UN) /RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN) . The results from this command are very close to those reported in Table 3 of the article. Now here's the bit that prompts my question: A comment in the syntax file says that "SPSS will not allow heterogeneous errors", and therefore, no attempt is made to fit model 2B. However, it seemed to me that with an appropriate /REPEATED sub-command, one should be able to fit model 2B. After a little tinkering around, I came up with this syntax: TITLE 'Table 3, Model 2B: Main Effects & Heterogeneous Errors'. MIXED lg_rt BY ID Item WITH c_mean c_sal oldage yrs65 /FIXED = c_mean c_sal oldage yrs65 /METHOD = ML /PRINT = SOLUTION TESTCOV R /RANDOM = INTERCEPT | SUBJECT(Item) COVTYPE(UN) /RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN) /REPEATED = oldage | SUBJECT(ID*Item) COVTYPE(DIAG) . This is giving me results that are very similar to the Model 2B results in Table 3 of the article, but it's not quite right. Notice that H&R's Model 2B has 10 parameters. Mine, on the other hand has only 9 parameters. So I'm missing something, but I can't figure out what it is. Ryan, I hope you're reading this--maybe you can spot it. In case it helps, here is the SAS code to run the same model--I assume the results reported in Table 3 are from SAS. TITLE 'SAS Model 1.2b: Main Effects Model with Heterogeneous Errors'; PROC MIXED DATA=Example.Ex1 COVTEST NOCLPRINT MAXITER=1000 METHOD=ML; CLASS ID Item older; MODEL lg_rt = c_mean c_sal oldage yrs65 / SOLUTION DDFM=Satterthwaite; RANDOM INTERCEPT / SUBJECT=Item TYPE=UN; RANDOM INTERCEPT / SUBJECT=ID TYPE=UN GROUP=older; REPEATED /SUBJECT=ID TYPE=VC GROUP=older; run; One thing I do notice is that the SAS code shows TYPE=VC on the REPEATED line. I assume TYPE refers to the covariance structure, and VC means variance components. AFAIK, the MIXED command in SPSS does not allow COVTYPE=VC on the /REPEATED line. From the FM: "If the variance components structure is specified on the REPEATED subcommand, it is replaced by the diagonal (DIAG) structure." So I wonder if VC vs DIAG is responsible for 10 vs 9 model parameters? Or is it something else about my /REPEATED line? I apologize again for posting such a long & complicated question--but I don't like seeing authors who don't use SPSS writing comments like "SPSS will not allow heterogeneous errors" when in fact it will! So I'd like to figure this out and let them know how to do it. ;-) Cheers, Bruce
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Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
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Hi Bruce, One thing that immediately stands out to me is that the second RANDOM statement in the SPSS MIXED code does not estimate "oldage"-specific covariance parameters. OTOH, the SAS MIXED code specifies "oldage"-specific covariance parameters by including the keyword "GROUP=" which increases the number of parameters being estimated by one, since there are presumably two age groups.
Ryan On Fri, Nov 22, 2013 at 5:29 PM, Bruce Weaver <[hidden email]> wrote: I apologize up front for the length & complexity of this post. Anyone who |
Re: Problem specifying MIXED model with heterogeneous variances
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Thanks Ryan. I may be missing the obvious, but how would you specify the model run by that SAS code in SPSS MIXED syntax? It is not a simple matter of changing the second /RANDOM line from
/RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN) to /RANDOM = INTERCEPT | SUBJECT(oldage) COVTYPE(UN) If I do that, the model won't run, and I get this warning: "The variables: oldage are specified both as subject variables in a RANDOM subcommand and as repeated measure variables in the REPEATED subcommand. Execution of this command stops." I wonder if life would be any easier trying this via GENLINMIXED?
--
Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
Re: Problem specifying MIXED model with heterogeneous variances
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Yes; I would look at the GROUPING keyword
on the RANDOM subcommand: http://pic.dhe.ibm.com/infocenter/spssstat/v22r0m0/topic/com.ibm.spss.statistics.reference/spss/advanced/syn_genlinmixed.htm
From: Bruce Weaver <[hidden email]> To: [hidden email], Date: 11/25/2013 10:31 AM Subject: Re: Problem specifying MIXED model with heterogeneous variances Sent by: "SPSSX(r) Discussion" <[hidden email]> Thanks Ryan. I may be missing the obvious, but how would you specify the model run by that SAS code in SPSS MIXED syntax? It is not a simple matter of changing the second /RANDOM line from /RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN) to /RANDOM = INTERCEPT | SUBJECT(oldage) COVTYPE(UN) If I do that, the model won't run, and I get this warning: "The variables: oldage are specified both as subject variables in a RANDOM subcommand and as repeated measure variables in the REPEATED subcommand. Execution of this command stops." I wonder if life would be any easier trying this via GENLINMIXED? Ryan Black wrote > Hi Bruce, > > One thing that immediately stands out to me is that the second RANDOM > statement in the SPSS MIXED code does not estimate "oldage"-specific > covariance parameters. OTOH, the SAS MIXED code specifies > "oldage"-specific covariance parameters by including the keyword "GROUP=" > which increases the number of parameters being estimated by one, since > there are presumably two age groups. > > Ryan > >> On Fri, Nov 22, 2013 at 5:29 PM, Bruce Weaver < > bruce.weaver@ > > wrote: >> I apologize up front for the length & complexity of this post. Anyone >> who >> decides to read it seriously is advised to have a cup (or maybe a pot) of >> strong coffee at the ready! ;-) >> >> I've been reading this article >> <http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1420&context=psychfacpub> >> by Hoffman & Rovine (2007), and looking at the SPSS syntax they provide >> here >> <http://psych.unl.edu/hoffman/Sheets/Research/MLM_for_Exp_Appendices.zip> >> . >> >> Table 3 in the article shows 3 models for analysis of data with repeated >> measures: >> >> 2A - Main effects only with homogeneous variances >> 2B - Main effects only with heterogeneous variances >> 3B - Main effects & selected interactions with heterogeneous variances >> >> The SPSS syntax for these models is found in file /MLM_AppendixA.sps/ >> (which >> is in the .zip from the link given above). Before anyone freaks out, let >> me >> point out that the data management steps in that syntax file could have >> been >> done a lot more efficiently. ;-) But that's not what I'm asking about. >> >> Here is the MIXED command they used to run model 2A above (note that they >> had command terminators on both /RANDOM sub-commands, and I had to remove >> the first one to get the model to run): >> >> MIXED lg_rt BY ID Item WITH c_mean c_sal oldage yrs65 >> /FIXED = c_mean c_sal oldage yrs65 >> /METHOD = ML >> /PRINT = SOLUTION TESTCOV R >> /RANDOM = INTERCEPT | SUBJECT(Item) COVTYPE(UN) >> /RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN) >> . >> >> The results from this command are very close to those reported in Table 3 >> of >> the article. >> >> Now here's the bit that prompts my question: A comment in the syntax >> file >> says that "SPSS will not allow heterogeneous errors", and therefore, no >> attempt is made to fit model 2B. However, it seemed to me that with an >> appropriate /REPEATED sub-command, one should be able to fit model 2B. >> After a little tinkering around, I came up with this syntax: >> >> TITLE 'Table 3, Model 2B: Main Effects & Heterogeneous Errors'. >> MIXED lg_rt BY ID Item WITH c_mean c_sal oldage yrs65 >> /FIXED = c_mean c_sal oldage yrs65 >> /METHOD = ML >> /PRINT = SOLUTION TESTCOV R >> /RANDOM = INTERCEPT | SUBJECT(Item) COVTYPE(UN) >> /RANDOM = INTERCEPT | SUBJECT(ID) COVTYPE(UN) >> * /REPEATED = oldage | SUBJECT(ID*Item) COVTYPE(DIAG)* >> . >> >> This is giving me results that are very similar to the Model 2B results >> in >> Table 3 of the article, but it's not quite right. Notice that H&R's >> Model >> 2B has 10 parameters. Mine, on the other hand has only 9 parameters. So >> I'm missing something, but I can't figure out what it is. >> >> Ryan, I hope you're reading this--maybe you can spot it. In case it >> helps, >> here is the SAS code to run the same model--I assume the results reported >> in >> Table 3 are from SAS. >> >> TITLE 'SAS Model 1.2b: Main Effects Model with Heterogeneous Errors'; >> PROC MIXED DATA=Example.Ex1 COVTEST NOCLPRINT MAXITER=1000 METHOD=ML; >> CLASS ID Item older; >> MODEL lg_rt = c_mean c_sal oldage yrs65 / SOLUTION DDFM=Satterthwaite; >> RANDOM INTERCEPT / SUBJECT=Item TYPE=UN; >> RANDOM INTERCEPT / SUBJECT=ID TYPE=UN GROUP=older; >> REPEATED /SUBJECT=ID TYPE=VC GROUP=older; run; >> >> One thing I do notice is that the SAS code shows TYPE=VC on the REPEATED >> line. I assume TYPE refers to the covariance structure, and VC means >> variance components. AFAIK, the MIXED command in SPSS does not allow >> COVTYPE=VC on the /REPEATED line. From the FM: >> >> "If the variance components structure is specified on the REPEATED >> subcommand, it is replaced by the >> diagonal (DIAG) structure." >> >> So I wonder if VC vs DIAG is responsible for 10 vs 9 model parameters? >> Or >> is it something else about my /REPEATED line? >> >> I apologize again for posting such a long & complicated question--but I >> don't like seeing authors who don't use SPSS writing comments like "SPSS >> will not allow heterogeneous errors" when in fact it will! So I'd like >> to >> figure this out and let them know how to do it. ;-) >> >> Cheers, >> Bruce >> >> >> >> >> >> ----- >> -- >> Bruce Weaver >> > bweaver@ >> 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/Problem-specifying-MIXED-model-with-heterogeneous-variances-tp5723261.html >> Sent from the SPSSX Discussion mailing list archive at Nabble.com. >> >> ===================== >> 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/Problem-specifying-MIXED-model-with-heterogeneous-variances-tp5723261p5723289.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 |
Re: Problem specifying MIXED model with heterogeneous variances
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Thanks Alex. A bunch of other stuff has cropped up, so I have to set this problem aside for a bit. But I'll certainly take a look at GENLINMIXED when I do come back to it.
Cheers, Bruce
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Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
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In reply to this post by Bruce Weaver
Bruce,  The code BELOW my name produces 10 parameter estimates and standard errors that are virtually identical to those reported in the article for model 2b. Note that there is a separate variance component for each level of "oldage" from the second RANDOM statement as is specified in the SAS MIXED code.
 Best, Ryan  -- RECODE oldage (0=1) (1=0) INTO oldage2. EXECUTE.   MIXED lg_rt BY ID Item WITH c_mean c_sal oldage yrs65 oldage2
  /FIXED = c_mean c_sal oldage yrs65   /METHOD = ML   /PRINT = SOLUTION TESTCOV R G   /RANDOM = INTERCEPT | SUBJECT(Item) COVTYPE(ID)   /RANDOM = oldage oldage2 | SUBJECT(ID)   /REPEATED = oldage | SUBJECT(ID*Item) COVTYPE(DIAG).  On Mon, Nov 25, 2013 at 10:28 AM, Bruce Weaver <[hidden email]> wrote: Thanks Ryan.  I may be missing the obvious, but how would you specify the |
Re: Problem specifying MIXED model with heterogeneous variances
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One does not need to specify the subject variable as random as SPSS does this automatically BUT using covtype(diag) instead of covtype(un) brings in the very unrealisitc assumption of homigeneity of variaiance etc. One of the (in my view major) advantage of mixed is that the unstructured covariance matrix takes care of variance heterogeneity automatically. This is true even for between group designs, and very useful as only oneway does this [not GLM] Best diana On 26/11/2013 03:01, "Ryan Black" <ryan.andrew.black@...> wrote: Bruce, Professor Diana Kornbrot email: : d.e.kornbrot@... web: http://dianakornbrot.wordpress.com/ http://go.herts.ac.uk/diana_kornbrot Work Department of Psychology School of Life and Medical Sciences University of Hertfordshire College Lane, Hatfield, Hertfordshire AL10 9AB, UK voice: +44 (0) 170 728 4626 Home 19 Elmhurst Avenue London N2 0LT, UK voice: +44 (0) 208 444 2081 mobile: +44 (0) 740 318 1612 |
Re: Problem specifying MIXED model with heterogeneous variances
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In reply to this post by Ryan
Yes, that does it. And just for completeness, COVTYPE = VC (the default for /RANDOM) on this line:
/RANDOM = oldage oldage2 | SUBJECT(ID) COVTYPE(VC) Thanks Ryan.
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Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
Re: Problem specifying MIXED model with heterogeneous variances
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In reply to this post by Kornbrot, Diana
Diana, I don't understand your statement, "...using covtype(diag) instead of covtype(un) brings in the very unrealisitc assumption of homigeneity of variaiance etc." The DIAG covariance type is used on the /REPEATED subcommand in that example, not /RANDOM:
/REPEATED = oldage | SUBJECT(ID*Item) COVTYPE(DIAG). And it is COVTYPE(DIAG) that allows heterogeneity of variance. From the list of covariance structures in the FM: DIAG Diagonal.This is a diagonal structure with heterogenous variance. This is the default covariance structure for repeated effects. (emphasis added) Cheers, Bruce
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Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
Re: Problem specifying MIXED model with heterogeneous variances
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In reply to this post by Bruce Weaver
Diana raised the topic of COVTYPE = UN (for unstructured). If I run Ryan's syntax but with COVTYPE(UN) rather than COVTYPE(VC), the Model Dimension table tells me there are 11 parameters rather than 10. However, one of those 11 parameters is a redundant covariance term that is equal to 0; so in reality, there are 10 parameters, and all estimates are identical to those from the first model with COVTYPE(VC).
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Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." PLEASE NOTE THE FOLLOWING: 1. My Hotmail account is not monitored regularly. To send me an e-mail, please use the address shown above. 2. The SPSSX Discussion forum on Nabble is no longer linked to the SPSSX-L listserv administered by UGA (https://listserv.uga.edu/). |
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