comparing growth of groups with varying numbers of repeated measures.
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comparing growth of groups with varying numbers of repeated measures.
 
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Does anybody have
(a) examples of studies and/or (b) experience with and/or (c) a text book citation that has a problem like this (d) a link to brief intro material for methods of comparing growth for 2 groups when there are different start points and different numbers of repeats for individuals. with some of the strings of repeats not completed yet. what I mean by different start points and numbers of repeats is that the data would look like this in wide layout (although it would most likely be wide layout since it is possible that covariate would also repeat). Project 1 to 30 are group1, project31 to 500 are group2. Easier to see in a fixed font. project covariate1 covariate2 covariate3 start_year #repeats completed money1 to moneywhatever 1 1955 1 1 1 22 y money1 to money22 2 1965 1 1 2 8 y money1 to money8 3 1990 10 3 1 21 y money1 to money22 4 2000 11 10 12 12 n money1 to money12 5 1990 5 5 5 7 y money1 to money7 6 2005 5 10 11 7 n money1 to money7 The research (alternate) hypothesis is that group1's money did not grow as quickly as group2's money even after controlling for covariates The null (default) hypothesis is that the 2 groups are not statistically distinguishable. -- Art Kendall Social Research Consultants
Art Kendall
Social Research Consultants |
Re: comparing growth of groups with varying numbers of repeated measures.
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Hi Art. I *think* you might find some useful examples in Singer & Willett's "Applied Longitudinal Data Analysis". The UCLA textbook examples page includes syntax for many of the examples in that book.
http://www.ats.ucla.edu/stat/spss/examples/alda/default.htm HTH.
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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 Art Kendall
Art, A linear mixed model (LMM) can certainly handle such a scenario. Before employing a LMM, however, I would suggest that you construct your dataset in vertical format with a numeric integer time variable that consists of sequential values from 0 through k, where 0 is the first year a subject was measured and k is the last year a subject was measured. Constructing the time variable as indicated above is not required.
Illustration: ID t y 1 0 <value> 1 1 <missing> 1 2 <value> 1 3 <value> 1 4 <value> 1 5 <value> 2 0 <missing> 2 1 <value> 2 2 <value> 2 3 <missing> 2 4 <value> 2 5 <value> . . . After constructing your dataset in vertical format (in their original time units or integer values as indicated above), the following MIXED code would be a reasonable place to start:
mixed y by group with time /fixed= time group time*group | sstype(3) /print= g r solution /random=time | subject(subject) covtype(un) /repeated= time | subject(subject) covtype(ar1). Much can be said about the parameterization above. In a nutshell, conditional upon subject-specific intercepts and slopes [which are permitted to covary], we assume decaying residual correlation as measurements become more temporally distant. Note, too, that time is being treated as a continuous variable which is accompanied by the usual implications. The test associated with the fixed effects interaction term will test the hypothesis of your primary research question. Ryan
On Sat, Dec 1, 2012 at 5:22 PM, Art Kendall <[hidden email]> wrote: Does anybody have |
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Not sure why that unfinished email was sent previously. I had started drafting a response yesterday, but didn't think it had been sent off. Anyway, the most recent message is what the OP and others should read. -Ryan
On Mon, Dec 3, 2012 at 3:00 PM, R B <[hidden email]> wrote:
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Re: comparing growth of groups with varying numbers of repeated measures.
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In reply to this post by Ryan
Ryan, I'm just curious about why you excluded "intercept" from your /RANDOM sub-command. I was thinking of the same type of model, but with a random intercept included. Thanks for clarifying.
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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Good catch, Bruce. The RANDOM statement should include the intercept term. The full RANDOM statement takes into account inter-individual variation at t0 (intercept term), inter-individual linear trajectory variation ("time" slope term), and for both random components to covary.
Ryan On Dec 3, 2012, at 5:39 PM, Bruce Weaver <[hidden email]> wrote: > Ryan, I'm just curious about why you excluded "intercept" from your /RANDOM > sub-command. I was thinking of the same type of model, but with a random > intercept included. Thanks for clarifying. > > Bruce > > > > R B wrote >> Art, >> >> A linear mixed model (LMM) can certainly handle such a scenario. Before >> employing a LMM, however, I would suggest that you construct your dataset >> in vertical format with a numeric integer time variable that consists >> of sequential values from 0 through k, where 0 is the first year a >> subject >> was measured and k is the last year a subject was measured. Constructing >> the time variable as indicated above is not required. >> >> Illustration: >> >> ID t y >> 1 0 >> <value> >> 1 1 >> <missing> >> 1 2 >> <value> >> 1 3 >> <value> >> 1 4 >> <value> >> 1 5 >> <value> >> 2 0 >> <missing> >> 2 1 >> <value> >> 2 2 >> <value> >> 2 3 >> <missing> >> 2 4 >> <value> >> 2 5 >> <value> >> . >> . >> . >> >> After constructing your dataset in vertical format (in their original >> time units or integer values as indicated above), the following MIXED code >> would be a reasonable place to start: >> >> mixed y by group with time >> /fixed= time group time*group | sstype(3) >> /print= g r solution >> /random=time | subject(subject) covtype(un) >> /repeated= time | subject(subject) covtype(ar1). >> >> Much can be said about the parameterization above. In a nutshell, >> conditional upon subject-specific intercepts and slopes [which are >> permitted to covary], we assume decaying residual correlation as >> measurements become more temporally distant. Note, too, that time is being >> treated as a continuous variable which is accompanied by the usual >> implications. >> The test associated with the fixed effects interaction term will test the >> hypothesis of your primary research question. >> Ryan >> On Sat, Dec 1, 2012 at 5:22 PM, Art Kendall < > >> Art@ > >> > wrote: >> >>> Does anybody have >>> (a) examples of studies and/or >>> (b) experience with and/or >>> (c) a text book citation that has a problem like this >>> (d) a link to brief intro material for methods of comparing growth >>> for 2 groups when there are different start points and different numbers >>> of repeats for individuals. with some of the strings of repeats not >>> completed yet. >>> >>> what I mean by different start points and numbers of repeats is that the >>> data would look like this in wide layout (although it would most likely >>> be wide layout since it is possible that covariate would also repeat). >>> Project 1 to 30 are group1, project31 to 500 are group2. >>> Easier to see in a fixed font. >>> project covariate1 covariate2 covariate3 start_year #repeats >>> completedmoney1 to moneywhatever >>> 1 1955 1 1 1 22 y money1 to money22 >>> 2 1965 1 1 2 8 y money1 to money8 >>> 3 1990 10 3 1 21 y money1 to money22 >>> 4 2000 11 10 12 12 n money1 to money12 >>> 5 1990 5 5 5 7 y money1 to money7 >>> 6 2005 5 10 11 7 n money1 to money7 >>> >>> The research (alternate) hypothesis is that group1's money did not grow >>> as quickly as group2's money even after controlling for covariates >>> The null (default) hypothesis is that the 2 groups are not statistically >>> distinguishable. >>> >>> -- >>> Art Kendall >>> Social Research Consultants >>> >>> >>> ------------------------------ >>> View this message in context: comparing growth of groups with varying >>> numbers of repeated >>> measures.<http://spssx-discussion.1045642.n5.nabble.com/comparing-growth-of-groups-with-varying-numbers-of-repeated-measures-tp5716577.html> >>> Sent from the SPSSX Discussion mailing list >>> archive<http://spssx-discussion.1045642.n5.nabble.com/>at >>> Nabble.com. > > > > > > ----- > -- > 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/comparing-growth-of-groups-with-varying-numbers-of-repeated-measures-tp5716577p5716622.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 |
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Okay, so I might as well just post what I'm thinking...Why random coefficient regression models (such as the one I proposed with that RANDOM statement) are often considered an intermediary step is because after we identify significant random variances and covariances, often, the next step is to incorporate 2nd level predictor(s) to help explain the variances and covariances. For example, random variances and covariances might be explained by, say, gender (a second-level predictor) of the subjects. Perhaps females tend to have higher mean levels at t0 as compared to males but have flatter linear trajectories as compared to males. Incorporation of a second-level predictor would then change the name of this model from a "random coefficient regression model" to a true "multilevel model."
Ryan On Mon, Dec 3, 2012 at 6:12 PM, <[hidden email]> wrote: Good catch, Bruce. The RANDOM statement should include the intercept term. The full RANDOM statement takes into account inter-individual variation at t0 (intercept term), inter-individual linear trajectory variation ("time" slope term), and for both random components to covary. |
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Actually, "group" (a time-invariant variable) is as a second-level predictor; I suppose the original model I proposed would in fact be classified as a multilevel model: mixed y by group with time /fixed= time group time*group | sstype(3) /print= g r solution /random=intercept time | subject(subject) covtype(un) /repeated= time | subject(subject) covtype(ar1). Ryan
On Mon, Dec 3, 2012 at 6:43 PM, R B <[hidden email]> wrote:
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Re: comparing growth of groups with varying numbers of repeated measures.
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In reply to this post by Ryan
Thank you for your
help. You confirmed what I expected.
I'll pass the message on the person working on
the project.
I just found out another complication. The DV in current dollars can never decrease from year to year, however, she does not know whether it can decrease in constant dollars. Any reactions to this? Art Kendall Social Research ConsultantsOn 12/3/2012 6:43 PM, R B wrote:
===================== 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
Art Kendall
Social Research Consultants |
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