mixed model not concave

[Yingyi Lin]

Hi Statalists,

I was trying to run a mixed model with Stata 15, however failed to do so with "not concave" error message.

The codes were simple:

mixed var1 var2 || id: var2

My total sample size is 700+, with 30 ids having repeated measures. I wonder if repeated observations (n=30+) nested within each id are insufficient sample size?

Thanks for any help in advance!
Yingyi

[Joseph Coveney]

I wonder if repeated observations (n=30+) nested within each id are insufficient sample size?

It seems that 30 ids each with 30 repeated observations is sufficient sample size for convergence (see below).

.ÿclearÿ*

.ÿ
.ÿsetÿseedÿ`=strreverse("1448922")'

.ÿ
.ÿquietlyÿdrawnormÿinterceptÿslope,ÿdoubleÿcorr(1ÿ-0.5ÿ\ÿ-0.5ÿ1)ÿn(30)

.ÿgenerateÿbyteÿidÿ=ÿ_n

.ÿ
.ÿquietlyÿexpandÿ30

.ÿ
.ÿgenerateÿdoubleÿvar2ÿ=ÿruniform()ÿ-ÿ0.5

.ÿgenerateÿdoubleÿvar1ÿ=ÿinterceptÿ+ÿvar2ÿ+ÿvar2ÿ*ÿslopeÿ+ÿrnormal()

.ÿ
.ÿmixedÿvar1ÿc.var2ÿ||ÿid:ÿvar2ÿ,ÿnolrtestÿnolog

Mixed-effectsÿMLÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿ900
Groupÿvariable:ÿidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿÿ30

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿ30
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ30.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿ30

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(1)ÿÿÿÿÿÿ=ÿÿÿÿÿÿ13.91
Logÿlikelihoodÿ=ÿ-1325.8725ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.0002

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿvar1ÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿvar2ÿ|ÿÿÿ.6816853ÿÿÿ.1827821ÿÿÿÿÿ3.73ÿÿÿ0.000ÿÿÿÿÿ.3234389ÿÿÿÿ1.039932
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ.1533372ÿÿÿ.1637727ÿÿÿÿÿ0.94ÿÿÿ0.349ÿÿÿÿ-.1676513ÿÿÿÿ.4743257
------------------------------------------------------------------------------

------------------------------------------------------------------------------
ÿÿRandom-effectsÿParametersÿÿ|ÿÿÿEstimateÿÿÿStd.ÿErr.ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-----------------------------+------------------------------------------------
id:ÿIndependentÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(var2)ÿ|ÿÿÿ.5677303ÿÿÿ.2479673ÿÿÿÿÿÿ.2411921ÿÿÿÿ1.336352
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(_cons)ÿ|ÿÿÿ.7714017ÿÿÿ.2077733ÿÿÿÿÿÿ.4550023ÿÿÿÿ1.307819
-----------------------------+------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(Residual)ÿ|ÿÿÿ.9737553ÿÿÿ.0474503ÿÿÿÿÿÿ.8850576ÿÿÿÿ1.071342
------------------------------------------------------------------------------

.ÿ
.ÿdisplayÿinÿsmclÿasÿtextÿe(converged)
1

.ÿ
.ÿexit

endÿofÿdo-file


.

But 30 × 30+ is closer to 900+ than to 700+.

[Weiwen Ng]

Stock advice in this case is to fit a simpler model, e.g. one with just a random intercept, then save the parameter estimates, then fit your random slopes model from the saved parameters as start values.

mixed var1 var2 || id:
matrix b = e(b)
mixed var1 var2 || id:, from(b)

I am assuming your log likelihood gets to a point where it's not visibly increasing, but you are getting "not concave" errors. If Stata still won't converge, one thing you can do is to find the point where that happens, then tell Stata to run only that number of iterations, then you can inspect the parameters to see what, specifically, is wrong. For example, say you hit 20 iterations, then the LL hits its asymptote. You can type:

mixed var1 var2 || id:, iterate(20)

Any parameter with a missing standard error is suspect. Of course, what to do about it can be less clear. If you can't get convergence after fitting the random intercept-only model, run the next bit of code and post the results in code delimiters, and we shall see if we can help.

[Yingyi Lin]

It seems that 30 ids each with 30 repeated observations is sufficient sample size for convergence (see below).

.ÿclearÿ*

.ÿ
.ÿsetÿseedÿ`=strreverse("1448922")'

.ÿ
.ÿquietlyÿdrawnormÿinterceptÿslope,ÿdoubleÿcorr(1ÿ-0.5ÿ\ÿ-0.5ÿ1)ÿn(30)

.ÿgenerateÿbyteÿidÿ=ÿ_n

.ÿ
.ÿquietlyÿexpandÿ30

.ÿ
.ÿgenerateÿdoubleÿvar2ÿ=ÿruniform()ÿ-ÿ0.5

.ÿgenerateÿdoubleÿvar1ÿ=ÿinterceptÿ+ÿvar2ÿ+ÿvar2ÿ*ÿslopeÿ+ÿrnormal()

.ÿ
.ÿmixedÿvar1ÿc.var2ÿ||ÿid:ÿvar2ÿ,ÿnolrtestÿnolog

Mixed-effectsÿMLÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿ900
Groupÿvariable:ÿidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿÿ30

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿ30
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ30.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿ30

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(1)ÿÿÿÿÿÿ=ÿÿÿÿÿÿ13.91
Logÿlikelihoodÿ=ÿ-1325.8725ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.0002

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿvar1ÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿvar2ÿ|ÿÿÿ.6816853ÿÿÿ.1827821ÿÿÿÿÿ3.73ÿÿÿ0.000ÿÿÿÿÿ.3234389ÿÿÿÿ1.039932
ÿÿÿÿÿÿÿ_consÿ|ÿÿÿ.1533372ÿÿÿ.1637727ÿÿÿÿÿ0.94ÿÿÿ0.349ÿÿÿÿ-.1676513ÿÿÿÿ.4743257
------------------------------------------------------------------------------

------------------------------------------------------------------------------
ÿÿRandom-effectsÿParametersÿÿ|ÿÿÿEstimateÿÿÿStd.ÿErr.ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-----------------------------+------------------------------------------------
id:ÿIndependentÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(var2)ÿ|ÿÿÿ.5677303ÿÿÿ.2479673ÿÿÿÿÿÿ.2411921ÿÿÿÿ1.336352
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(_cons)ÿ|ÿÿÿ.7714017ÿÿÿ.2077733ÿÿÿÿÿÿ.4550023ÿÿÿÿ1.307819
-----------------------------+------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿvar(Residual)ÿ|ÿÿÿ.9737553ÿÿÿ.0474503ÿÿÿÿÿÿ.8850576ÿÿÿÿ1.071342
------------------------------------------------------------------------------

.ÿ
.ÿdisplayÿinÿsmclÿasÿtextÿe(converged)
1

.ÿ
.ÿexit

endÿofÿdo-file


.

But 30 × 30+ is closer to 900+ than to 700+.

Hey Joseph, thanks for your reply. My total sample size is 700+ (level 1: study participants), and repeated measures (repeated twice) within only 30 participants (level 2). I wonder if 30 is too small here to successfully converge? Thanks.

[Yingyi Lin]

Hey Weiwen, thanks for your reply and I tried your simpler codes and they worked! Thanks again!

[Fred Lee]

Stock advice in this case is to fit a simpler model, e.g. one with just a random intercept, then save the parameter estimates, then fit your random slopes model from the saved parameters as start values.

mixed var1 var2 || id:
matrix b = e(b)
mixed var1 var2 || id:, from(b)

I am assuming your log likelihood gets to a point where it's not visibly increasing, but you are getting "not concave" errors. If Stata still won't converge, one thing you can do is to find the point where that happens, then tell Stata to run only that number of iterations, then you can inspect the parameters to see what, specifically, is wrong. For example, say you hit 20 iterations, then the LL hits its asymptote. You can type:

mixed var1 var2 || id:, iterate(20)

Any parameter with a missing standard error is suspect. Of course, what to do about it can be less clear. If you can't get convergence after fitting the random intercept-only model, run the next bit of code and post the results in code delimiters, and we shall see if we can help.

why when I use the from option of mixed, the Stata shows that option from() not allowed
thanks

[Joseph Coveney]

why when I use the from option of mixed, the Stata shows that option from() not allowed

mixed doesn't allow from() for starting values. If you want to use that option to fit a hierarchical linear model, then you can use meglm.