Dear all,

I am trying to fit a mixed model to longitudinal data from a field
study. Over a course of 2 weeks patients were asked 3 times a day
(pseudo-randomly) to give subjective data (all likert-scales). Because
it is a repeated design, I would want to allow for correlated
residuals. Further, I would want to allow for heterogeneous variances,
because of possible situation specific factors affecting measurements.

From how I understand the literature I thought of the following model
(SPSS-syntax):

MIXED
   V1 BY V2
   /CRITERIA = CIN(95) MXITER(100) MXSTEP(5) SCORING(1)
   SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(0,
ABSOLUTE)
   PCONVERGE(0.000001, ABSOLUTE)
   /FIXED = V2 | SSTYPE(3)
   /METHOD = REML
   /PRINT = SOLUTION TESTCOV
   /REPEATED = time | SUBJECT(id) COVTYPE(ARH1) .

For the moment, I am just interested in the interrelations of those
variables, i.e. the effect of V2.

Does this make sense?

Thank you very much.

Kind regards,
Ruben

On Jan 20, 12:30=A0pm, Ruben <real.ru...@googlemail.com> wrote:
> Dear all,
>
> I am trying to fit a mixed model to longitudinal data from a field
> study. Over a course of 2 weeks patients were asked 3 times a day
> (pseudo-randomly) to give subjective data (all likert-scales). Because
> it is a repeated design, I would want to allow for correlated
> residuals. Further, I would want to allow for heterogeneous variances,
> because of possible situation specific factors affecting measurements.
>
> From how I understand the literature I thought of the following model
> (SPSS-syntax):
>
> MIXED
> =A0 =A0V1 BY V2
> =A0 =A0/CRITERIA =3D CIN(95) MXITER(100) MXSTEP(5) SCORING(1)
> =A0 =A0SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(0,
> ABSOLUTE)
> =A0 =A0PCONVERGE(0.000001, ABSOLUTE)
> =A0 =A0/FIXED =3D V2 | SSTYPE(3)
> =A0 =A0/METHOD =3D REML
> =A0 =A0/PRINT =3D SOLUTION TESTCOV
> =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE(ARH1) .
>
> For the moment, I am just interested in the interrelations of those
> variables, i.e. the effect of V2.
>
> Does this make sense?
>
> Thank you very much.
>
> Kind regards,
> Ruben

Ruben,

Generally, I do not believe an AR residual variance-covariance matrix
is appropriate for data that are collected at unequally spaced
intervals. Note that I said generally an AR type is not appropriate,
but given that the assessment points are so close to each other, an AR
type might suffice. If you were using SAS, I'd probably recommend that
you consider a spatial variance-covariance matrix. As far as I'm
aware, SPSS does not offer this type of matrix. Another option would
be to specify an unstructured matrix.

HTH,

Ryan

On Jan 23, 2:40=A0am, Ryan <ryan.andrew.bl...@gmail.com> wrote:
> On Jan 20, 12:30=A0pm, Ruben <real.ru...@googlemail.com> wrote:
>
>
>
> > Dear all,
>
> > I am trying to fit a mixed model to longitudinal data from a field
> > study. Over a course of 2 weeks patients were asked 3 times a day
> > (pseudo-randomly) to give subjective data (all likert-scales). Because
> > it is a repeated design, I would want to allow for correlated
> > residuals. Further, I would want to allow for heterogeneous variances,
> > because of possible situation specific factors affecting measurements.
>
> > From how I understand the literature I thought of the following model
> > (SPSS-syntax):
>
> > MIXED
> > =A0 =A0V1 BY V2
> > =A0 =A0/CRITERIA =3D CIN(95) MXITER(100) MXSTEP(5) SCORING(1)
> > =A0 =A0SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(0,
> > ABSOLUTE)
> > =A0 =A0PCONVERGE(0.000001, ABSOLUTE)
> > =A0 =A0/FIXED =3D V2 | SSTYPE(3)
> > =A0 =A0/METHOD =3D REML
> > =A0 =A0/PRINT =3D SOLUTION TESTCOV
> > =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE(ARH1) .
>
> > For the moment, I am just interested in the interrelations of those
> > variables, i.e. the effect of V2.
>
> > Does this make sense?
>
> > Thank you very much.
>
> > Kind regards,
> > Ruben
>
> Ruben,
>
> Generally, I do not believe an AR residual variance-covariance matrix
> is appropriate for data that are collected at unequally spaced
> intervals. Note that I said generally an AR type is not appropriate,
> but given that the assessment points are so close to each other, an AR
> type might suffice. If you were using SAS, I'd probably recommend that
> you consider a spatial variance-covariance matrix. As far as I'm
> aware, SPSS does not offer this type of matrix. Another option would
> be to specify an unstructured matrix.
>
> HTH,
>
> Ryan

Dear Ryan,

thanks for the reply. I tend to agree that AR type matrices are
difficult with uneven spaced intervals. I refrained from using UN
because of fear of overfitting the model. As of now, i'd prefer
compound symmetry, i.e. dropping assumptions of time-dependent
covariances but maintaining overall covariance.
I should rely check if SAS might not be more appropriate.

Thanks again for your reply.

Ruben

On Jan 23, 5:50=A0am, Ruben <real.ru...@googlemail.com> wrote:
> On Jan 23, 2:40=A0am, Ryan <ryan.andrew.bl...@gmail.com> wrote:
>
>
>
>
>
> > On Jan 20, 12:30=A0pm, Ruben <real.ru...@googlemail.com> wrote:
>
> > > Dear all,
>
> > > I am trying to fit a mixed model to longitudinal data from a field
> > > study. Over a course of 2 weeks patients were asked 3 times a day
> > > (pseudo-randomly) to give subjective data (all likert-scales). Becaus=
e
> > > it is a repeated design, I would want to allow for correlated
> > > residuals. Further, I would want to allow for heterogeneous variances=
,
> > > because of possible situation specific factors affecting measurements=
..
>
> > > From how I understand the literature I thought of the following model
> > > (SPSS-syntax):
>
> > > MIXED
> > > =A0 =A0V1 BY V2
> > > =A0 =A0/CRITERIA =3D CIN(95) MXITER(100) MXSTEP(5) SCORING(1)
> > > =A0 =A0SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(0,
> > > ABSOLUTE)
> > > =A0 =A0PCONVERGE(0.000001, ABSOLUTE)
> > > =A0 =A0/FIXED =3D V2 | SSTYPE(3)
> > > =A0 =A0/METHOD =3D REML
> > > =A0 =A0/PRINT =3D SOLUTION TESTCOV
> > > =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE(ARH1) .
>
> > > For the moment, I am just interested in the interrelations of those
> > > variables, i.e. the effect of V2.
>
> > > Does this make sense?
>
> > > Thank you very much.
>
> > > Kind regards,
> > > Ruben
>
> > Ruben,
>
> > Generally, I do not believe an AR residual variance-covariance matrix
> > is appropriate for data that are collected at unequally spaced
> > intervals. Note that I said generally an AR type is not appropriate,
> > but given that the assessment points are so close to each other, an AR
> > type might suffice. If you were using SAS, I'd probably recommend that
> > you consider a spatial variance-covariance matrix. As far as I'm
> > aware, SPSS does not offer this type of matrix. Another option would
> > be to specify an unstructured matrix.
>
> > HTH,
>
> > Ryan
>
> Dear Ryan,
>
> thanks for the reply. I tend to agree that AR type matrices are
> difficult with uneven spaced intervals. I refrained from using UN
> because of fear of overfitting the model. As of now, i'd prefer
> compound symmetry, i.e. dropping assumptions of time-dependent
> covariances but maintaining overall covariance.
> I should rely check if SAS might not be more appropriate.
>
> Thanks again for your reply.
>
> Ruben- Hide quoted text -
>
> - Show quoted text -

Ruben,

It is possible to test statistically if a model (i.e. with AR residual
matrix) that is nested within another model (i.e. with UN residual
matrix) has a significantly better or worse fit. This test is known as
a likelihood ratio test. The likelihood ratio test is constructed by
taking the difference in -2 log likelihoods estimated for each model.
The difference in -2 log likelihoods approximates a Chi-Square
distribution with degrees of freedom equal to the difference in the #
of estimated parameters for each model. The likelihood ratio test has
a few assumptions including (a) a relatively large sample size, (b)
nested models [as mentioned previously], and (c) the same exact data
used when testing each model.

The model you present above is far from the full model. Are you sure
that time should not be added as a fixed effect as well? Along those
lines, have you considered the possibility of an interaction effect,
V2-BY-time? Perhaps the relatationship between V2 and V1 depends upon
time?

Well, if you wanted to treat time as a categorical variable within the
full model, one way to set up the code would be:

MIXED
   V1 BY V2 time
   /FIXED =3D V2 time V2*time | SSTYPE(3)
   /METHOD =3D REML
   /PRINT =3D SOLUTION TESTCOV
   /REPEATED =3D time | SUBJECT(id) COVTYPE({you specify}) .

You could also treat time as a covariate, but that assumes there is a
linear relationship between time and V1. At any rate, the full model
would look like this:

MIXED
   V1 BY V2 WITH time
   /FIXED =3D V2 time V2*time | SSTYPE(3)
   /METHOD =3D REML
   /PRINT =3D SOLUTION TESTCOV
   /REPEATED =3D time | SUBJECT(id) COVTYPE({you specify}) .

You could, of course, build higher terms which would allow you to test
non-linear relationships between time and V1.

All of this is mere speculation because I don't know much about your
data. My hope is that this post will remind you that there are many
possible parameterizations, some of which could yield better fitting
models than the one you proposed originally.

Ryan

On 23 Jan., 14:32, Ryan <ryan.andrew.bl...@gmail.com> wrote:
> On Jan 23, 5:50=A0am, Ruben <real.ru...@googlemail.com> wrote:
>
>
>
> > On Jan 23, 2:40=A0am, Ryan <ryan.andrew.bl...@gmail.com> wrote:
>
> > > On Jan 20, 12:30=A0pm, Ruben <real.ru...@googlemail.com> wrote:
>
> > > > Dear all,
>
> > > > I am trying to fit a mixed model to longitudinal data from a field
> > > > study. Over a course of 2 weeks patients were asked 3 times a day
> > > > (pseudo-randomly) to give subjective data (all likert-scales). Beca=
use
> > > > it is a repeated design, I would want to allow for correlated
> > > > residuals. Further, I would want to allow for heterogeneous varianc=
es,
> > > > because of possible situation specific factors affecting measuremen=
ts.
>
> > > > From how I understand the literature I thought of the following mod=
el
> > > > (SPSS-syntax):
>
> > > > MIXED
> > > > =A0 =A0V1 BY V2
> > > > =A0 =A0/CRITERIA =3D CIN(95) MXITER(100) MXSTEP(5) SCORING(1)
> > > > =A0 =A0SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(0,
> > > > ABSOLUTE)
> > > > =A0 =A0PCONVERGE(0.000001, ABSOLUTE)
> > > > =A0 =A0/FIXED =3D V2 | SSTYPE(3)
> > > > =A0 =A0/METHOD =3D REML
> > > > =A0 =A0/PRINT =3D SOLUTION TESTCOV
> > > > =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE(ARH1) .
>
> > > > For the moment, I am just interested in the interrelations of those
> > > > variables, i.e. the effect of V2.
>
> > > > Does this make sense?
>
> > > > Thank you very much.
>
> > > > Kind regards,
> > > > Ruben
>
> > > Ruben,
>
> > > Generally, I do not believe an AR residual variance-covariance matrix
> > > is appropriate for data that are collected at unequally spaced
> > > intervals. Note that I said generally an AR type is not appropriate,
> > > but given that the assessment points are so close to each other, an A=
R
> > > type might suffice. If you were using SAS, I'd probably recommend tha=
t
> > > you consider a spatial variance-covariance matrix. As far as I'm
> > > aware, SPSS does not offer this type of matrix. Another option would
> > > be to specify an unstructured matrix.
>
> > > HTH,
>
> > > Ryan
>
> > Dear Ryan,
>
> > thanks for the reply. I tend to agree that AR type matrices are
> > difficult with uneven spaced intervals. I refrained from using UN
> > because of fear of overfitting the model. As of now, i'd prefer
> > compound symmetry, i.e. dropping assumptions of time-dependent
> > covariances but maintaining overall covariance.
> > I should rely check if SAS might not be more appropriate.
>
> > Thanks again for your reply.
>
> > Ruben- Hide quoted text -
>
> > - Show quoted text -
>
> Ruben,
>
> It is possible to test statistically if a model (i.e. with AR residual
> matrix) that is nested within another model (i.e. with UN residual
> matrix) has a significantly better or worse fit. This test is known as
> a likelihood ratio test. The likelihood ratio test is constructed by
> taking the difference in -2 log likelihoods estimated for each model.
> The difference in -2 log likelihoods approximates a Chi-Square
> distribution with degrees of freedom equal to the difference in the #
> of estimated parameters for each model. The likelihood ratio test has
> a few assumptions including (a) a relatively large sample size, (b)
> nested models [as mentioned previously], and (c) the same exact data
> used when testing each model.
>
> The model you present above is far from the full model. Are you sure
> that time should not be added as a fixed effect as well? Along those
> lines, have you considered the possibility of an interaction effect,
> V2-BY-time? Perhaps the relatationship between V2 and V1 depends upon
> time?
>
> Well, if you wanted to treat time as a categorical variable within the
> full model, one way to set up the code would be:
>
> MIXED
> =A0 =A0V1 BY V2 time
> =A0 =A0/FIXED =3D V2 time V2*time | SSTYPE(3)
> =A0 =A0/METHOD =3D REML
> =A0 =A0/PRINT =3D SOLUTION TESTCOV
> =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE({you specify}) .
>
> You could also treat time as a covariate, but that assumes there is a
> linear relationship between time and V1. At any rate, the full model
> would look like this:
>
> MIXED
> =A0 =A0V1 BY V2 WITH time
> =A0 =A0/FIXED =3D V2 time V2*time | SSTYPE(3)
> =A0 =A0/METHOD =3D REML
> =A0 =A0/PRINT =3D SOLUTION TESTCOV
> =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE({you specify}) .
>
> You could, of course, build higher terms which would allow you to test
> non-linear relationships between time and V1.
>
> All of this is mere speculation because I don't know much about your
> data. My hope is that this post will remind you that there are many
> possible parameterizations, some of which could yield better fitting
> models than the one you proposed originally.
>
> Ryan

Dear Ryan,

thanks again for your post. I know my model is far from being the full
model. I also know about the LRT, in fact i am using it to compare
ARH1 with AR1. BTW, do you know of any references indicating which
covariance structures are nested? I was trying to find out whether CS
is nested in AR1. I think it is not, i just couldn't find any
reference.
Unfortunately, i cannot use UN because i lack subjects.

The idea of my model was simply to indicate a relationship between V1
& V2. I know that with V2 beeing a categorical variable i could have
used repeated measures t-tests. With continous variables there is a
possibility of OLS-regressing V1 on V2 within each subject, saving
regression parameters and calculating the mean parameters across
subjects. Problem with this approach, or averaging correlations, is
that information on the goodness of fit of the individual regression
within each subject is lost. To make a long story short, i wanted to
use mixed models to express a simple linear relationship between V1 &
V2 while taking information on goodness of fit into account.
So actually, i am not interested in the effect of time, i just use it
to indicate repeated observations of V1 & V2. This is why i didn't
model effects of time and its interaction with V2.

So my question would be rather whether it's possible to "abuse" mixed
models in the way proposed. What do you think?

Thanks again for your suggestions.

Ruben

On Jan 25, 8:55=A0am, Ruben <real.ru...@googlemail.com> wrote:
> On 23 Jan., 14:32, Ryan <ryan.andrew.bl...@gmail.com> wrote:
>
>
>
>
>
> > On Jan 23, 5:50=A0am, Ruben <real.ru...@googlemail.com> wrote:
>
> > > On Jan 23, 2:40=A0am, Ryan <ryan.andrew.bl...@gmail.com> wrote:
>
> > > > On Jan 20, 12:30=A0pm, Ruben <real.ru...@googlemail.com> wrote:
>
> > > > > Dear all,
>
> > > > > I am trying to fit a mixed model to longitudinal data from a fiel=
d
> > > > > study. Over a course of 2 weeks patients were asked 3 times a day
> > > > > (pseudo-randomly) to give subjective data (all likert-scales). Be=
cause
> > > > > it is a repeated design, I would want to allow for correlated
> > > > > residuals. Further, I would want to allow for heterogeneous varia=
nces,
> > > > > because of possible situation specific factors affecting measurem=
ents.
>
> > > > > From how I understand the literature I thought of the following m=
odel
> > > > > (SPSS-syntax):
>
> > > > > MIXED
> > > > > =A0 =A0V1 BY V2
> > > > > =A0 =A0/CRITERIA =3D CIN(95) MXITER(100) MXSTEP(5) SCORING(1)
> > > > > =A0 =A0SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(=
0,
> > > > > ABSOLUTE)
> > > > > =A0 =A0PCONVERGE(0.000001, ABSOLUTE)
> > > > > =A0 =A0/FIXED =3D V2 | SSTYPE(3)
> > > > > =A0 =A0/METHOD =3D REML
> > > > > =A0 =A0/PRINT =3D SOLUTION TESTCOV
> > > > > =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE(ARH1) .
>
> > > > > For the moment, I am just interested in the interrelations of tho=
se
> > > > > variables, i.e. the effect of V2.
>
> > > > > Does this make sense?
>
> > > > > Thank you very much.
>
> > > > > Kind regards,
> > > > > Ruben
>
> > > > Ruben,
>
> > > > Generally, I do not believe an AR residual variance-covariance matr=
ix
> > > > is appropriate for data that are collected at unequally spaced
> > > > intervals. Note that I said generally an AR type is not appropriate=
,
> > > > but given that the assessment points are so close to each other, an=
 AR
> > > > type might suffice. If you were using SAS, I'd probably recommend t=
hat
> > > > you consider a spatial variance-covariance matrix. As far as I'm
> > > > aware, SPSS does not offer this type of matrix. Another option woul=
d
> > > > be to specify an unstructured matrix.
>
> > > > HTH,
>
> > > > Ryan
>
> > > Dear Ryan,
>
> > > thanks for the reply. I tend to agree that AR type matrices are
> > > difficult with uneven spaced intervals. I refrained from using UN
> > > because of fear of overfitting the model. As of now, i'd prefer
> > > compound symmetry, i.e. dropping assumptions of time-dependent
> > > covariances but maintaining overall covariance.
> > > I should rely check if SAS might not be more appropriate.
>
> > > Thanks again for your reply.
>
> > > Ruben- Hide quoted text -
>
> > > - Show quoted text -
>
> > Ruben,
>
> > It is possible to test statistically if a model (i.e. with AR residual
> > matrix) that is nested within another model (i.e. with UN residual
> > matrix) has a significantly better or worse fit. This test is known as
> > a likelihood ratio test. The likelihood ratio test is constructed by
> > taking the difference in -2 log likelihoods estimated for each model.
> > The difference in -2 log likelihoods approximates a Chi-Square
> > distribution with degrees of freedom equal to the difference in the #
> > of estimated parameters for each model. The likelihood ratio test has
> > a few assumptions including (a) a relatively large sample size, (b)
> > nested models [as mentioned previously], and (c) the same exact data
> > used when testing each model.
>
> > The model you present above is far from the full model. Are you sure
> > that time should not be added as a fixed effect as well? Along those
> > lines, have you considered the possibility of an interaction effect,
> > V2-BY-time? Perhaps the relatationship between V2 and V1 depends upon
> > time?
>
> > Well, if you wanted to treat time as a categorical variable within the
> > full model, one way to set up the code would be:
>
> > MIXED
> > =A0 =A0V1 BY V2 time
> > =A0 =A0/FIXED =3D V2 time V2*time | SSTYPE(3)
> > =A0 =A0/METHOD =3D REML
> > =A0 =A0/PRINT =3D SOLUTION TESTCOV
> > =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE({you specify}) .
>
> > You could also treat time as a covariate, but that assumes there is a
> > linear relationship between time and V1. At any rate, the full model
> > would look like this:
>
> > MIXED
> > =A0 =A0V1 BY V2 WITH time
> > =A0 =A0/FIXED =3D V2 time V2*time | SSTYPE(3)
> > =A0 =A0/METHOD =3D REML
> > =A0 =A0/PRINT =3D SOLUTION TESTCOV
> > =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE({you specify}) .
>
> > You could, of course, build higher terms which would allow you to test
> > non-linear relationships between time and V1.
>
> > All of this is mere speculation because I don't know much about your
> > data. My hope is that this post will remind you that there are many
> > possible parameterizations, some of which could yield better fitting
> > models than the one you proposed originally.
>
> > Ryan
>
> Dear Ryan,
>
> thanks again for your post. I know my model is far from being the full
> model. I also know about the LRT, in fact i am using it to compare
> ARH1 with AR1. BTW, do you know of any references indicating which
> covariance structures are nested? I was trying to find out whether CS
> is nested in AR1. I think it is not, i just couldn't find any
> reference.
> Unfortunately, i cannot use UN because i lack subjects.
>
> The idea of my model was simply to indicate a relationship between V1
> & V2. I know that with V2 beeing a categorical variable i could have
> used repeated measures t-tests. With continous variables there is a
> possibility of OLS-regressing V1 on V2 within each subject, saving
> regression parameters and calculating the mean parameters across
> subjects. Problem with this approach, or averaging correlations, is
> that information on the goodness of fit of the individual regression
> within each subject is lost. To make a long story short, i wanted to
> use mixed models to express a simple linear relationship between V1 &
> V2 while taking information on goodness of fit into account.
> So actually, i am not interested in the effect of time, i just use it
> to indicate repeated observations of V1 & V2. This is why i didn't
> model effects of time and its interaction with V2.
>
> So my question would be rather whether it's possible to "abuse" mixed
> models in the way proposed. What do you think?
>
> Thanks again for your suggestions.
>
> Ruben- Hide quoted text -
>
> - Show quoted text -

Ruben,

A CS residual matrix is NOT nested within an AR residual matrix. For
non-nested models you can compare overall fit by examining AIC and BIC
(similar to -2LL, lower means better). If you determine that the CS
matrix is the way to proceed *and* you have no (or very, very little)
data missing at random (MAR), then you might consider running a
repeated measures ANOVA. However, if you find that any other residual
matrix is more appropriate and/or you have MAR data, then you should
probably stick with mixed models. If you have missing data that are
NOT missing at random, then all bets are off.

Again, I am assuming that you've met assumptions to run a linear mixed
model (including a large enough sample size). If you have met
assumptions, then I don't see anything wrong with running a linear
mixed model to test if there is a statistically significant linear
relationship between V1 and V2, while taking into account within-
subject correlation of error terms.

Ryan

On Jan 25, 6:09=A0pm, Ryan <ryan.andrew.bl...@gmail.com> wrote:
> On Jan 25, 8:55=A0am, Ruben <real.ru...@googlemail.com> wrote:
>
>
>
>
>
> > On 23 Jan., 14:32, Ryan <ryan.andrew.bl...@gmail.com> wrote:
>
> > > On Jan 23, 5:50=A0am, Ruben <real.ru...@googlemail.com> wrote:
>
> > > > On Jan 23, 2:40=A0am, Ryan <ryan.andrew.bl...@gmail.com> wrote:
>
> > > > > On Jan 20, 12:30=A0pm, Ruben <real.ru...@googlemail.com> wrote:
>
> > > > > > Dear all,
>
> > > > > > I am trying to fit a mixed model to longitudinal data from a fi=
eld
> > > > > > study. Over a course of 2 weeks patients were asked 3 times a d=
ay
> > > > > > (pseudo-randomly) to give subjective data (all likert-scales). =
Because
> > > > > > it is a repeated design, I would want to allow for correlated
> > > > > > residuals. Further, I would want to allow for heterogeneous var=
iances,
> > > > > > because of possible situation specific factors affecting measur=
ements.
>
> > > > > > From how I understand the literature I thought of the following=
 model
> > > > > > (SPSS-syntax):
>
> > > > > > MIXED
> > > > > > =A0 =A0V1 BY V2
> > > > > > =A0 =A0/CRITERIA =3D CIN(95) MXITER(100) MXSTEP(5) SCORING(1)
> > > > > > =A0 =A0SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERG=
E(0,
> > > > > > ABSOLUTE)
> > > > > > =A0 =A0PCONVERGE(0.000001, ABSOLUTE)
> > > > > > =A0 =A0/FIXED =3D V2 | SSTYPE(3)
> > > > > > =A0 =A0/METHOD =3D REML
> > > > > > =A0 =A0/PRINT =3D SOLUTION TESTCOV
> > > > > > =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE(ARH1) .
>
> > > > > > For the moment, I am just interested in the interrelations of t=
hose
> > > > > > variables, i.e. the effect of V2.
>
> > > > > > Does this make sense?
>
> > > > > > Thank you very much.
>
> > > > > > Kind regards,
> > > > > > Ruben
>
> > > > > Ruben,
>
> > > > > Generally, I do not believe an AR residual variance-covariance ma=
trix
> > > > > is appropriate for data that are collected at unequally spaced
> > > > > intervals. Note that I said generally an AR type is not appropria=
te,
> > > > > but given that the assessment points are so close to each other, =
an AR
> > > > > type might suffice. If you were using SAS, I'd probably recommend=
 that
> > > > > you consider a spatial variance-covariance matrix. As far as I'm
> > > > > aware, SPSS does not offer this type of matrix. Another option wo=
uld
> > > > > be to specify an unstructured matrix.
>
> > > > > HTH,
>
> > > > > Ryan
>
> > > > Dear Ryan,
>
> > > > thanks for the reply. I tend to agree that AR type matrices are
> > > > difficult with uneven spaced intervals. I refrained from using UN
> > > > because of fear of overfitting the model. As of now, i'd prefer
> > > > compound symmetry, i.e. dropping assumptions of time-dependent
> > > > covariances but maintaining overall covariance.
> > > > I should rely check if SAS might not be more appropriate.
>
> > > > Thanks again for your reply.
>
> > > > Ruben- Hide quoted text -
>
> > > > - Show quoted text -
>
> > > Ruben,
>
> > > It is possible to test statistically if a model (i.e. with AR residua=
l
> > > matrix) that is nested within another model (i.e. with UN residual
> > > matrix) has a significantly better or worse fit. This test is known a=
s
> > > a likelihood ratio test. The likelihood ratio test is constructed by
> > > taking the difference in -2 log likelihoods estimated for each model.
> > > The difference in -2 log likelihoods approximates a Chi-Square
> > > distribution with degrees of freedom equal to the difference in the #
> > > of estimated parameters for each model. The likelihood ratio test has
> > > a few assumptions including (a) a relatively large sample size, (b)
> > > nested models [as mentioned previously], and (c) the same exact data
> > > used when testing each model.
>
> > > The model you present above is far from the full model. Are you sure
> > > that time should not be added as a fixed effect as well? Along those
> > > lines, have you considered the possibility of an interaction effect,
> > > V2-BY-time? Perhaps the relatationship between V2 and V1 depends upon
> > > time?
>
> > > Well, if you wanted to treat time as a categorical variable within th=
e
> > > full model, one way to set up the code would be:
>
> > > MIXED
> > > =A0 =A0V1 BY V2 time
> > > =A0 =A0/FIXED =3D V2 time V2*time | SSTYPE(3)
> > > =A0 =A0/METHOD =3D REML
> > > =A0 =A0/PRINT =3D SOLUTION TESTCOV
> > > =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE({you specify}) .
>
> > > You could also treat time as a covariate, but that assumes there is a
> > > linear relationship between time and V1. At any rate, the full model
> > > would look like this:
>
> > > MIXED
> > > =A0 =A0V1 BY V2 WITH time
> > > =A0 =A0/FIXED =3D V2 time V2*time | SSTYPE(3)
> > > =A0 =A0/METHOD =3D REML
> > > =A0 =A0/PRINT =3D SOLUTION TESTCOV
> > > =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE({you specify}) .
>
> > > You could, of course, build higher terms which would allow you to tes=
t
> > > non-linear relationships between time and V1.
>
> > > All of this is mere speculation because I don't know much about your
> > > data. My hope is that this post will remind you that there are many
> > > possible parameterizations, some of which could yield better fitting
> > > models than the one you proposed originally.
>
> > > Ryan
>
> > Dear Ryan,
>
> > thanks again for your post. I know my model is far from being the full
> > model. I also know about the LRT, in fact i am using it to compare
> > ARH1 with AR1. BTW, do you know of any references indicating which
> > covariance structures are nested? I was trying to find out whether CS
> > is nested in AR1. I think it is not, i just couldn't find any
> > reference.
> > Unfortunately, i cannot use UN because i lack subjects.
>
> > The idea of my model was simply to indicate a relationship between V1
> > & V2. I know that with V2 beeing a categorical variable i could have
> > used repeated measures t-tests. With continous variables there is a
> > possibility of OLS-regressing V1 on V2 within each subject, saving
> > regression parameters and calculating the mean parameters across
> > subjects. Problem with this approach, or averaging correlations, is
> > that information on the goodness of fit of the individual regression
> > within each subject is lost. To make a long story short, i wanted to
> > use mixed models to express a simple linear relationship between V1 &
> > V2 while taking information on goodness of fit into account.
> > So actually, i am not interested in the effect of time, i just use it
> > to indicate repeated observations of V1 & V2. This is why i didn't
> > model effects of time and its interaction with V2.
>
> > So my question would be rather whether it's possible to "abuse" mixed
> > models in the way proposed. What do you think?
>
> > Thanks again for your suggestions.
>
> > Ruben- Hide quoted text -
>
> > - Show quoted text -
>
> Ruben,
>
> A CS residual matrix is NOT nested within an AR residual matrix. For
> non-nested models you can compare overall fit by examining AIC and BIC
> (similar to -2LL, lower means better). If you determine that the CS
> matrix is the way to proceed *and* you have no (or very, very little)
> data missing at random (MAR), then you might consider running a
> repeated measures ANOVA. However, if you find that any other residual
> matrix is more appropriate and/or you have MAR data, then you should
> probably stick with mixed models. If you have missing data that are
> NOT missing at random, then all bets are off.
>
> Again, I am assuming that you've met assumptions to run a linear mixed
> model (including a large enough sample size). If you have met
> assumptions, then I don't see anything wrong with running a linear
> mixed model to test if there is a statistically significant linear
> relationship between V1 and V2, while taking into account within-
> subject correlation of error terms.
>
> Ryan

Ruben

To clarify my last post, since V2 is treated as a categorical
variable, a significant coefficient will indicate the means are
significantly different. Exactly which means are different depends on
the reference group etc.

Ryan
Ryan

On 26 Jan., 02:38, Ryan <ryan.andrew.bl...@gmail.com> wrote:
> On Jan 25, 6:09=A0pm, Ryan <ryan.andrew.bl...@gmail.com> wrote:
>
>
>
> > On Jan 25, 8:55=A0am, Ruben <real.ru...@googlemail.com> wrote:
>
> > > On 23 Jan., 14:32, Ryan <ryan.andrew.bl...@gmail.com> wrote:
>
> > > > On Jan 23, 5:50=A0am, Ruben <real.ru...@googlemail.com> wrote:
>
> > > > > On Jan 23, 2:40=A0am, Ryan <ryan.andrew.bl...@gmail.com> wrote:
>
> > > > > > On Jan 20, 12:30=A0pm, Ruben <real.ru...@googlemail.com> wrote:
>
> > > > > > > Dear all,
>
> > > > > > > I am trying to fit a mixed model to longitudinal data from a =
field
> > > > > > > study. Over a course of 2 weeks patients were asked 3 times a=
 day
> > > > > > > (pseudo-randomly) to give subjective data (all likert-scales)=
.. Because
> > > > > > > it is a repeated design, I would want to allow for correlated
> > > > > > > residuals. Further, I would want to allow for heterogeneous v=
ariances,
> > > > > > > because of possible situation specific factors affecting meas=
urements.
>
> > > > > > > From how I understand the literature I thought of the followi=
ng model
> > > > > > > (SPSS-syntax):
>
> > > > > > > MIXED
> > > > > > > =A0 =A0V1 BY V2
> > > > > > > =A0 =A0/CRITERIA =3D CIN(95) MXITER(100) MXSTEP(5) SCORING(1)
> > > > > > > =A0 =A0SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVE=
RGE(0,
> > > > > > > ABSOLUTE)
> > > > > > > =A0 =A0PCONVERGE(0.000001, ABSOLUTE)
> > > > > > > =A0 =A0/FIXED =3D V2 | SSTYPE(3)
> > > > > > > =A0 =A0/METHOD =3D REML
> > > > > > > =A0 =A0/PRINT =3D SOLUTION TESTCOV
> > > > > > > =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE(ARH1) .
>
> > > > > > > For the moment, I am just interested in the interrelations of=
 those
> > > > > > > variables, i.e. the effect of V2.
>
> > > > > > > Does this make sense?
>
> > > > > > > Thank you very much.
>
> > > > > > > Kind regards,
> > > > > > > Ruben
>
> > > > > > Ruben,
>
> > > > > > Generally, I do not believe an AR residual variance-covariance =
matrix
> > > > > > is appropriate for data that are collected at unequally spaced
> > > > > > intervals. Note that I said generally an AR type is not appropr=
iate,
> > > > > > but given that the assessment points are so close to each other=
, an AR
> > > > > > type might suffice. If you were using SAS, I'd probably recomme=
nd that
> > > > > > you consider a spatial variance-covariance matrix. As far as I'=
m
> > > > > > aware, SPSS does not offer this type of matrix. Another option =
would
> > > > > > be to specify an unstructured matrix.
>
> > > > > > HTH,
>
> > > > > > Ryan
>
> > > > > Dear Ryan,
>
> > > > > thanks for the reply. I tend to agree that AR type matrices are
> > > > > difficult with uneven spaced intervals. I refrained from using UN
> > > > > because of fear of overfitting the model. As of now, i'd prefer
> > > > > compound symmetry, i.e. dropping assumptions of time-dependent
> > > > > covariances but maintaining overall covariance.
> > > > > I should rely check if SAS might not be more appropriate.
>
> > > > > Thanks again for your reply.
>
> > > > > Ruben- Hide quoted text -
>
> > > > > - Show quoted text -
>
> > > > Ruben,
>
> > > > It is possible to test statistically if a model (i.e. with AR resid=
ual
> > > > matrix) that is nested within another model (i.e. with UN residual
> > > > matrix) has a significantly better or worse fit. This test is known=
 as
> > > > a likelihood ratio test. The likelihood ratio test is constructed b=
y
> > > > taking the difference in -2 log likelihoods estimated for each mode=
l.
> > > > The difference in -2 log likelihoods approximates a Chi-Square
> > > > distribution with degrees of freedom equal to the difference in the=
 #
> > > > of estimated parameters for each model. The likelihood ratio test h=
as
> > > > a few assumptions including (a) a relatively large sample size, (b)
> > > > nested models [as mentioned previously], and (c) the same exact dat=
a
> > > > used when testing each model.
>
> > > > The model you present above is far from the full model. Are you sur=
e
> > > > that time should not be added as a fixed effect as well? Along thos=
e
> > > > lines, have you considered the possibility of an interaction effect=
,
> > > > V2-BY-time? Perhaps the relatationship between V2 and V1 depends up=
on
> > > > time?
>
> > > > Well, if you wanted to treat time as a categorical variable within =
the
> > > > full model, one way to set up the code would be:
>
> > > > MIXED
> > > > =A0 =A0V1 BY V2 time
> > > > =A0 =A0/FIXED =3D V2 time V2*time | SSTYPE(3)
> > > > =A0 =A0/METHOD =3D REML
> > > > =A0 =A0/PRINT =3D SOLUTION TESTCOV
> > > > =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE({you specify}) .
>
> > > > You could also treat time as a covariate, but that assumes there is=
 a
> > > > linear relationship between time and V1. At any rate, the full mode=
l
> > > > would look like this:
>
> > > > MIXED
> > > > =A0 =A0V1 BY V2 WITH time
> > > > =A0 =A0/FIXED =3D V2 time V2*time | SSTYPE(3)
> > > > =A0 =A0/METHOD =3D REML
> > > > =A0 =A0/PRINT =3D SOLUTION TESTCOV
> > > > =A0 =A0/REPEATED =3D time | SUBJECT(id) COVTYPE({you specify}) .
>
> > > > You could, of course, build higher terms which would allow you to t=
est
> > > > non-linear relationships between time and V1.
>
> > > > All of this is mere speculation because I don't know much about you=
r
> > > > data. My hope is that this post will remind you that there are many
> > > > possible parameterizations, some of which could yield better fittin=
g
> > > > models than the one you proposed originally.
>
> > > > Ryan
>
> > > Dear Ryan,
>
> > > thanks again for your post. I know my model is far from being the ful=
l
> > > model. I also know about the LRT, in fact i am using it to compare
> > > ARH1 with AR1. BTW, do you know of any references indicating which
> > > covariance structures are nested? I was trying to find out whether CS
> > > is nested in AR1. I think it is not, i just couldn't find any
> > > reference.
> > > Unfortunately, i cannot use UN because i lack subjects.
>
> > > The idea of my model was simply to indicate a relationship between V1
> > > & V2. I know that with V2 beeing a categorical variable i could have
> > > used repeated measures t-tests. With continous variables there is a
> > > possibility of OLS-regressing V1 on V2 within each subject, saving
> > > regression parameters and calculating the mean parameters across
> > > subjects. Problem with this approach, or averaging correlations, is
> > > that information on the goodness of fit of the individual regression
> > > within each subject is lost. To make a long story short, i wanted to
> > > use mixed models to express a simple linear relationship between V1 &
> > > V2 while taking information on goodness of fit into account.
> > > So actually, i am not interested in the effect of time, i just use it
> > > to indicate repeated observations of V1 & V2. This is why i didn't
> > > model effects of time and its interaction with V2.
>
> > > So my question would be rather whether it's possible to "abuse" mixed
> > > models in the way proposed. What do you think?
>
> > > Thanks again for your suggestions.
>
> > > Ruben- Hide quoted text -
>
> > > - Show quoted text -
>
> > Ruben,
>
> > A CS residual matrix is NOT nested within an AR residual matrix. For
> > non-nested models you can compare overall fit by examining AIC and BIC
> > (similar to -2LL, lower means better). If you determine that the CS
> > matrix is the way to proceed *and* you have no (or very, very little)
> > data missing at random (MAR), then you might consider running a
> > repeated measures ANOVA. However, if you find that any other residual
> > matrix is more appropriate and/or you have MAR data, then you should
> > probably stick with mixed models. If you have missing data that are
> > NOT missing at random, then all bets are off.
>
> > Again, I am assuming that you've met assumptions to run a linear mixed
> > model (including a large enough sample size). If you have met
> > assumptions, then I don't see anything wrong with running a linear
> > mixed model to test if there is a statistically significant linear
> > relationship between V1 and V2, while taking into account within-
> > subject correlation of error terms.
>
> > Ryan
>
> Ruben
>
> To clarify my last post, since V2 is treated as a categorical
> variable, a significant coefficient will indicate the means are
> significantly different. Exactly which means are different depends on
> the reference group etc.
>
> Ryan
> Ryan

Dear Ryan,

thanks a lot for your help.

Ruben