Question about the loglike_twas function in your src CoMM_covar_pxem_ptr.cpp

yuanzhongshang commented 6 years ago

Hi, Sorry for interrupting you. This is zhongshang Yuan. In source code CoMM_covar_pxem_ptr.cpp, the definition of the fucntion loglike_twas is confused with me.

Since the loglikelihood function are used for the LRT test, the loglike_twas fucntion should be the incomplete likelihood (i.e. the observed likelihood), which should integrate out the latent variable u from the expression (6). However, the definition in your code seems quite different.

Furthermore, the definition looks quite similar with the expression (9), However, the trace term in expression (9) has been missed and it is not equal to the term "sum(log(R.diag()))".

Would you like to explain this to me?

Thanks a lot. I am looking forward to your reply.

gordonliu810822 commented 6 years ago

Dear Zhongshang, I checked the expression for in-complete-data log-likelihood. There is no problems after integrating out \mu. Thanks for your interest.

Best, Jin

Jin Liu, PhD Assistant Professor Center of Quantitative Medicine Duke-NUS Medical School 20 College Road, Academia, Level 6, Room 57 Singapore, 169856 Tel: +65 6576 7376 Fax:+65 6225 1244 Email: jin.liu@duke-nus.edu.sgmailto:jin.liu@duke-nus.edu.sg Homepage: https://sites.google.com/site/liujin810822/

On Sat, Oct 27, 2018 at 9:00 AM yuanzhongshang notifications@github.com<mailto:notifications@github.com> wrote:

Hi, Sorry for interrupting you. This is zhongshang Yuan. In source code CoMM_covar_pxem_ptr.cpp, the definition of the fucntion loglike_twas is confused with me.

Since the loglikelihood function are used for the LRT test, the loglike_twas fucntion should be the incomplete likelihood (i.e. the observed likelihood), which should integrate out the latent variable u from the expression (6). However, the definition in your code seems quite different.

Furthermore, the definition looks quite similar with the expression (10), However, the trace term in expression (10) has been missed and it is not equal to the term "sum(log(R.diag()))".

Would you like to explain this to me?

Thanks a lot.

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gordonliu810822 commented 6 years ago

To be specific, you can take h = [y;z] and w = [w_1;\alpha w_2]. Then h ~ N(x\mu, \Sigma_e\otimes I). You can integrate \mu here and find the expression for the marginal likelihood.

Jin Liu, PhD Assistant Professor Center of Quantitative Medicine Duke-NUS Medical School 20 College Road, Academia, Level 6, Room 57 Singapore, 169856 Tel: +65 6576 7376 Fax:+65 6225 1244 Email: jin.liu@duke-nus.edu.sgmailto:jin.liu@duke-nus.edu.sg Homepage: https://sites.google.com/site/liujin810822/

On Sun, Oct 28, 2018 at 1:22 PM Jin Liu jin.liu@duke-nus.edu.sg<mailto:jin.liu@duke-nus.edu.sg> wrote: Dear Zhongshang, I checked the expression for in-complete-data log-likelihood. There is no problems after integrating out \mu. Thanks for your interest.

Best, Jin

Jin Liu, PhD Assistant Professor Center of Quantitative Medicine Duke-NUS Medical School 20 College Road, Academia, Level 6, Room 57 Singapore, 169856 Tel: +65 6576 7376 Fax:+65 6225 1244 Email: jin.liu@duke-nus.edu.sgmailto:jin.liu@duke-nus.edu.sg Homepage: https://sites.google.com/site/liujin810822/

On Sat, Oct 27, 2018 at 9:00 AM yuanzhongshang notifications@github.com<mailto:notifications@github.com> wrote:

Hi, Sorry for interrupting you. This is zhongshang Yuan. In source code CoMM_covar_pxem_ptr.cpp, the definition of the fucntion loglike_twas is confused with me.

Since the loglikelihood function are used for the LRT test, the loglike_twas fucntion should be the incomplete likelihood (i.e. the observed likelihood), which should integrate out the latent variable u from the expression (6). However, the definition in your code seems quite different.

Furthermore, the definition looks quite similar with the expression (10), However, the trace term in expression (10) has been missed and it is not equal to the term "sum(log(R.diag()))".

Would you like to explain this to me?

Thanks a lot.

— You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHubhttps://github.com/gordonliu810822/CoMM/issues/1, or mute the threadhttps://github.com/notifications/unsubscribe-auth/AK2u3hyfaJcMlZMSA2GnGTi1qQaVFS41ks5uo7AbgaJpZM4X9KbY.

Important: This email is confidential and may be privileged. If you are not the intended recipient, please delete it and notify us immediately; you should not copy or use it for any purpose, nor disclose its contents to any other person. Thank you.

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