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From |
Gillian.Frost@hsl.gov.uk |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Exercise 7.10 in Multilevel and Longitudinal Modeling Using Stata (first edition) |

Date |
Tue, 9 Mar 2010 09:45:02 +0000 |

Hello all, Looking further into my original query to Statalist (below), I have come across an exercise in the Stata book "Multilevel and Longitudinal Modeling Using Stata" by Rabe-Hesketh & Skrondal, which I think can help. However, I am struggling with the exercise (exercise 7.10 Peak-expiratory-flow data I) and have been unable to find the solutions to see where I am going wrong. Part 2 of the exercise asks you to verify that the two level model (with the variances of the two random coefficients constrained equal and if the covariance is positive) is equivalent to the three level model, but I have been unable to do this. Please see the code and output below from the models I have used. As you can see, the models do not appear to be equivalent. However, I do not understand where I have made an error. I would hugely appreciate any help with this, as this is proving to be a huge stumbling block for me. Many thanks, Gillian ***************** Start Stata code ** Section 7.2 multilevel modelling book use http://www.stata-press.com/data/mlmus/pefr, clear reshape long wp wm, i(id) j(occassion) gen i = _n reshape long w, i(i) j(meth) string sort id meth occassion list id meth occassion w in 1/8, clean noobs encode meth, gen(method) recode method 2=0 * section 7.4.4 - three level model xtmixed w || id: || method:, mle * exercise 7.10 * two level model tab method, gen(m) xtmixed w || id: m1 m2, mle cov(exch) ****************** Output ** Three level model Performing EM optimization: Performing gradient-based optimization: Iteration 0: log likelihood = -345.29139 Iteration 1: log likelihood = -345.29005 Iteration 2: log likelihood = -345.29005 Computing standard errors: Mixed-effects ML regression Number of obs = 68 ----------------------------------------------------------- | No. of Observations per Group Group Variable | Groups Minimum Average Maximum ----------------+------------------------------------------ id | 17 4 4.0 4 method | 34 2 2.0 2 ----------------------------------------------------------- Wald chi2(0) = . Log likelihood = -345.29005 Prob > chi2 = . ------------------------------------------------------------------------------ w | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- _cons | 450.8971 26.63839 16.93 0.000 398.6868 503.1074 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ id: Identity | sd(_cons) | 108.6037 19.05411 77.00246 153.1739 -----------------------------+------------------------------------------------ method: Identity | sd(_cons) | 19.47623 4.829488 11.97937 31.66474 -----------------------------+------------------------------------------------ sd(Residual) | 17.75859 2.153545 14.00184 22.52329 ------------------------------------------------------------------------------ LR test vs. linear regression: chi2(2) = 143.81 Prob > chi2 = 0.0000 Note: LR test is conservative and provided only for reference. ** Two level model note: m2 dropped because of collinearity Performing EM optimization: Performing gradient-based optimization: Iteration 0: log likelihood = -355.14961 Iteration 1: log likelihood = -355.14961 Computing standard errors: Mixed-effects ML regression Number of obs = 68 Group variable: id Number of groups = 17 Obs per group: min = 4 avg = 4.0 max = 4 Wald chi2(0) = . Log likelihood = -355.14961 Prob > chi2 = . ------------------------------------------------------------------------------ w | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- _cons | 454.0498 19.42288 23.38 0.000 415.9817 492.118 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ id: Exchangeable | sd(m1 _cons) | 79.12354 9.858542 61.97959 101.0096 corr(m1,_cons) | .0489807 .2547191 -.4230663 .500116 -----------------------------+------------------------------------------------ sd(Residual) | 17.67097 2.122189 13.96483 22.36069 ------------------------------------------------------------------------------ LR test vs. linear regression: chi2(2) = 124.10 Prob > chi2 = 0.0000 Note: LR test is conservative and provided only for reference. ----- Forwarded by Gillian Frost/STAFF/HSL on 09/03/2010 09:25 ----- Gillian.Frost@hsl.gov.uk Sent by: owner-statalist@hsphsun2.harvard.edu 08/03/2010 12:00 Please respond to statalist@hsphsun2.harvard.edu To statalist@hsphsun2.harvard.edu cc Subject st: -xtmixed- and differences in test-retest reliability Hello all, I was wondering if anyone would be able to help me with a problem I have. I know that there must be some way to do this, but I cannot for the life of me figure out how to do it. A brief explanation of data: Altogether there are about 40 subjects. Each subject underwent a test to assess their hearing on three different days, three times each day. The goal is to assess the reliability of the test (its reproducibility), as well as any between day or within day variation in test results. I know that I can use xtmixed to estimate a variance-components model, the results of which can be used to estimate the test-retest reliability, the between days (within subject) intraclass correlation coefficient (ICC), and the within day ICC. I would use the following model: xtmixed result || subject: || day: Now here is where I am getting confused. What if I also wanted to know if the test-retest reliability differed depending on some other factor? For example, what if (for some reason) the test was more reliable for males than females? Or more reliable for older age groups than younger ones? How would I test for this? I suppose I could use separate models for males and females, but how could I then test whether the ICCs were statistically significantly different? Any help with this matter would be greatly appreciated. Please just ask if anything needs clarifying. Many thanks, Gillian ------------------------------------------------------------------------ ATTENTION: This message contains privileged and confidential information intended for the addressee(s) only. If this message was sent to you in error, you must not disseminate, copy or take any action in reliance on it and we request that you notify the sender immediately by return email. Opinions expressed in this message and any attachments are not necessarily those held by the Health and Safety Laboratory or any person connected with the organisation, save those by whom the opinions were expressed. 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If this message was sent to you in error, you must not disseminate, copy or take any action in reliance on it and we request that you notify the sender immediately by return email. Opinions expressed in this message and any attachments are not necessarily those held by the Health and Safety Laboratory or any person connected with the organisation, save those by whom the opinions were expressed. Please note that any messages sent or received by the Health and Safety Laboratory email system may be monitored and stored in an information retrieval system. ------------------------------------------------------------------------ Think before you print - do you really need to print this email? ------------------------------------------------------------------------ ------------------------------------------------------------------------ Scanned by MailMarshal - Marshal's comprehensive email content security solution. 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