That's true but if he uses some AIC or BIC criterion that penalizes the number of parameters, then he might see something else ? This ( comparing mixtures to not mixtures ) is not something I deal with so I'm just throwing it out there. On Tue, Sep 22, 2015 at 4:30 PM, Bert Gunter <bgunter.4567 at gmail.com> wrote:> Two normals will **always** be a better fit than one, as the latter > must be a subset of the former (with identical parameters for both > normals). > > Cheers, > Bert > > > Bert Gunter > > "Data is not information. Information is not knowledge. And knowledge > is certainly not wisdom." > -- Clifford Stoll > > > On Tue, Sep 22, 2015 at 1:21 PM, John Sorkin > <JSorkin at grecc.umaryland.edu> wrote: > > I have data that may be the mixture of two normal distributions (one > contained within the other) vs. a single normal. > > I used normalmixEM to get estimates of parameters assuming two normals: > > > > > > GLUT <- scale(na.omit(data[,"FCW_glut"])) > > GLUT > > mixmdl = normalmixEM(GLUT,k=1,arbmean=TRUE) > > summary(mixmdl) > > plot(mixmdl,which=2) > > lines(density(data[,"GLUT"]), lty=2, lwd=2) > > > > > > > > > > > > summary of normalmixEM object: > > comp 1 comp 2 > > lambda 0.7035179 0.296482 > > mu -0.0592302 0.140545 > > sigma 1.1271620 0.536076 > > loglik at estimate: -110.8037 > > > > > > > > I would like to see if the two normal distributions are a better fit > that one normal. I have two problems > > (1) normalmixEM does not seem to what to fit a single normal (even if I > address the error message produced): > > > > > >> mixmdl = normalmixEM(GLUT,k=1) > > Error in normalmix.init(x = x, lambda = lambda, mu = mu, s = sigma, k > k, : > > arbmean and arbvar cannot both be FALSE > >> mixmdl = normalmixEM(GLUT,k=1,arbmean=TRUE) > > Error in normalmix.init(x = x, lambda = lambda, mu = mu, s = sigma, k > k, : > > arbmean and arbvar cannot both be FALSE > > > > > > > > (2) Even if I had the loglik from a single normal, I am not sure how > many DFs to use when computing the -2LL ratio test. > > > > > > Any suggestions for comparing the two-normal vs. one normal distribution > would be appreciated. > > > > > > Thanks > > John > > > > > > > > > > > > > > > > > > > > John David Sorkin M.D., Ph.D. > > Professor of Medicine > > Chief, Biostatistics and Informatics > > University of Maryland School of Medicine Division of Gerontology and > Geriatric Medicine > > Baltimore VA Medical Center > > 10 North Greene Street > > GRECC (BT/18/GR) > > Baltimore, MD 21201-1524 > > (Phone) 410-605-7119 > > (Fax) 410-605-7913 (Please call phone number above prior to faxing) > > > > > > Confidentiality Statement: > > This email message, including any attachments, is for ...{{dropped:12}} > > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. >[[alternative HTML version deleted]]
I am not sure AIC or BIC would be needed as the two normal distribution has at least two additional parameters to estimate; mean 1, var1, mean 2, var 2 where as the one normal has to estimate only var1 and var2.In any event, I don't know how to fit the single normal and get values for the loglik let alone AIC or BIC John John David Sorkin M.D., Ph.D. Professor of Medicine Chief, Biostatistics and Informatics University of Maryland School of Medicine Division of Gerontology and Geriatric Medicine Baltimore VA Medical Center 10 North Greene Street GRECC (BT/18/GR) Baltimore, MD 21201-1524 (Phone) 410-605-7119 (Fax) 410-605-7913 (Please call phone number above prior to faxing)>>> Mark Leeds <markleeds2 at gmail.com> 09/22/15 4:36 PM >>>That's true but if he uses some AIC or BIC criterion that penalizes the number of parameters, then he might see something else ? This ( comparing mixtures to not mixtures ) is not something I deal with so I'm just throwing it out there. On Tue, Sep 22, 2015 at 4:30 PM, Bert Gunter <bgunter.4567 at gmail.com> wrote: Two normals will **always** be a better fit than one, as the latter must be a subset of the former (with identical parameters for both normals). Cheers, Bert Bert Gunter "Data is not information. Information is not knowledge. And knowledge is certainly not wisdom." -- Clifford Stoll On Tue, Sep 22, 2015 at 1:21 PM, John Sorkin <JSorkin at grecc.umaryland.edu> wrote: > I have data that may be the mixture of two normal distributions (one contained within the other) vs. a single normal. > I used normalmixEM to get estimates of parameters assuming two normals: > > > GLUT <- scale(na.omit(data[,"FCW_glut"])) > GLUT > mixmdl = normalmixEM(GLUT,k=1,arbmean=TRUE) > summary(mixmdl) > plot(mixmdl,which=2) > lines(density(data[,"GLUT"]), lty=2, lwd=2) > > > > > > summary of normalmixEM object: > comp 1 comp 2 > lambda 0.7035179 0.296482 > mu -0.0592302 0.140545 > sigma 1.1271620 0.536076 > loglik at estimate: -110.8037 > > > > I would like to see if the two normal distributions are a better fit that one normal. I have two problems > (1) normalmixEM does not seem to what to fit a single normal (even if I address the error message produced): > > >> mixmdl = normalmixEM(GLUT,k=1) > Error in normalmix.init(x = x, lambda = lambda, mu = mu, s = sigma, k = k, : > arbmean and arbvar cannot both be FALSE >> mixmdl = normalmixEM(GLUT,k=1,arbmean=TRUE) > Error in normalmix.init(x = x, lambda = lambda, mu = mu, s = sigma, k = k, : > arbmean and arbvar cannot both be FALSE > > > > (2) Even if I had the loglik from a single normal, I am not sure how many DFs to use when computing the -2LL ratio test. > > > Any suggestions for comparing the two-normal vs. one normal distribution would be appreciated. > > > Thanks > John > > > > > > > > > > John David Sorkin M.D., Ph.D. > Professor of Medicine > Chief, Biostatistics and Informatics > University of Maryland School of Medicine Division of Gerontology and Geriatric Medicine > Baltimore VA Medical Center > 10 North Greene Street > GRECC (BT/18/GR) > Baltimore, MD 21201-1524 > (Phone) 410-605-7119410-605-7119 > (Fax) 410-605-7913 (Please call phone number above prior to faxing) > > > Confidentiality Statement:> This email message, including any attachments, is for ...{{dropped:12}}______________________________________________ R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Call Send SMS Call from mobile Add to Skype You'll need Skype CreditFree via Skype Confidentiality Statement: This email message, including any attachments, is for the sole use of the intended recipient(s) and may contain confidential and privileged information. Any unauthorized use, disclosure or distribution is prohibited. If you are not the intended recipient, please contact the sender by reply email and destroy all copies of the original message.
I'll be brief in my reply to you both, as this is off topic. So what? All this statistical stuff is irrelevant baloney(and of questionable accuracy, since based on asymptotics and strong assumptions, anyway) . The question of interest is whether a mixture fit better suits the context, which only the OP knows and which none of us can answer. I know that many will disagree with this -- maybe a few might agree -- but please send all replies, insults, praise, and learned discourse to me privately, as I have already occupied more space on the list than I should. Cheers, Bert Bert Gunter "Data is not information. Information is not knowledge. And knowledge is certainly not wisdom." -- Clifford Stoll On Tue, Sep 22, 2015 at 1:35 PM, Mark Leeds <markleeds2 at gmail.com> wrote:> That's true but if he uses some AIC or BIC criterion that penalizes the > number of parameters, > then he might see something else ? This ( comparing mixtures to not mixtures > ) is not something I deal with so I'm just throwing it out there. > > > > > On Tue, Sep 22, 2015 at 4:30 PM, Bert Gunter <bgunter.4567 at gmail.com> wrote: >> >> Two normals will **always** be a better fit than one, as the latter >> must be a subset of the former (with identical parameters for both >> normals). >> >> Cheers, >> Bert >> >> >> Bert Gunter >> >> "Data is not information. Information is not knowledge. And knowledge >> is certainly not wisdom." >> -- Clifford Stoll >> >> >> On Tue, Sep 22, 2015 at 1:21 PM, John Sorkin >> <JSorkin at grecc.umaryland.edu> wrote: >> > I have data that may be the mixture of two normal distributions (one >> > contained within the other) vs. a single normal. >> > I used normalmixEM to get estimates of parameters assuming two normals: >> > >> > >> > GLUT <- scale(na.omit(data[,"FCW_glut"])) >> > GLUT >> > mixmdl = normalmixEM(GLUT,k=1,arbmean=TRUE) >> > summary(mixmdl) >> > plot(mixmdl,which=2) >> > lines(density(data[,"GLUT"]), lty=2, lwd=2) >> > >> > >> > >> > >> > >> > summary of normalmixEM object: >> > comp 1 comp 2 >> > lambda 0.7035179 0.296482 >> > mu -0.0592302 0.140545 >> > sigma 1.1271620 0.536076 >> > loglik at estimate: -110.8037 >> > >> > >> > >> > I would like to see if the two normal distributions are a better fit >> > that one normal. I have two problems >> > (1) normalmixEM does not seem to what to fit a single normal (even if I >> > address the error message produced): >> > >> > >> >> mixmdl = normalmixEM(GLUT,k=1) >> > Error in normalmix.init(x = x, lambda = lambda, mu = mu, s = sigma, k >> > k, : >> > arbmean and arbvar cannot both be FALSE >> >> mixmdl = normalmixEM(GLUT,k=1,arbmean=TRUE) >> > Error in normalmix.init(x = x, lambda = lambda, mu = mu, s = sigma, k >> > k, : >> > arbmean and arbvar cannot both be FALSE >> > >> > >> > >> > (2) Even if I had the loglik from a single normal, I am not sure how >> > many DFs to use when computing the -2LL ratio test. >> > >> > >> > Any suggestions for comparing the two-normal vs. one normal distribution >> > would be appreciated. >> > >> > >> > Thanks >> > John >> > >> > >> > >> > >> > >> > >> > >> > >> > >> > John David Sorkin M.D., Ph.D. >> > Professor of Medicine >> > Chief, Biostatistics and Informatics >> > University of Maryland School of Medicine Division of Gerontology and >> > Geriatric Medicine >> > Baltimore VA Medical Center >> > 10 North Greene Street >> > GRECC (BT/18/GR) >> > Baltimore, MD 21201-1524 >> > (Phone) 410-605-7119 >> > (Fax) 410-605-7913 (Please call phone number above prior to faxing) >> > >> > >> > Confidentiality Statement: >> > This email message, including any attachments, is for ...{{dropped:12}} >> >> ______________________________________________ >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide >> http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. > >
Bert I am surprised by your response. Statistics serves two purposes: estimation and hypothesis testing. Sometimes we are fortunate and theory, physiology, physics, or something else tell us what is the correct, or perhaps I should same most adequate model. Sometimes theory fails us and we wish to choose between two competing models. This is my case. The cell sizes may come from one normal distribution (theory 1) or two (theory 2). Choosing between the models will help us postulate about physiology. I want to use statistics to help me decide between the two competing models, and thus inform my understanding of physiology. It is true that statistics can't tell me which model is the "correct" or "true" model, but it should be able to help me select the more "adequate" or "appropriate" or "closer to he truth" model. In any event, I still don't know how to fit a single normal distribution and get a measure of fit e.g. log likelihood. John John David Sorkin M.D., Ph.D. Professor of Medicine Chief, Biostatistics and Informatics University of Maryland School of Medicine Division of Gerontology and Geriatric Medicine Baltimore VA Medical Center 10 North Greene Street GRECC (BT/18/GR) Baltimore, MD 21201-1524 (Phone) 410-605-7119 (Fax) 410-605-7913 (Please call phone number above prior to faxing)>>> Bert Gunter <bgunter.4567 at gmail.com> 09/22/15 4:48 PM >>>I'll be brief in my reply to you both, as this is off topic. So what? All this statistical stuff is irrelevant baloney(and of questionable accuracy, since based on asymptotics and strong assumptions, anyway) . The question of interest is whether a mixture fit better suits the context, which only the OP knows and which none of us can answer. I know that many will disagree with this -- maybe a few might agree -- but please send all replies, insults, praise, and learned discourse to me privately, as I have already occupied more space on the list than I should. Cheers, Bert Bert Gunter "Data is not information. Information is not knowledge. And knowledge is certainly not wisdom." -- Clifford Stoll On Tue, Sep 22, 2015 at 1:35 PM, Mark Leeds <markleeds2 at gmail.com> wrote:> That's true but if he uses some AIC or BIC criterion that penalizes the > number of parameters, > then he might see something else ? This ( comparing mixtures to not mixtures > ) is not something I deal with so I'm just throwing it out there. > > > > > On Tue, Sep 22, 2015 at 4:30 PM, Bert Gunter <bgunter.4567 at gmail.com> wrote: >> >> Two normals will **always** be a better fit than one, as the latter >> must be a subset of the former (with identical parameters for both >> normals). >> >> Cheers, >> Bert >> >> >> Bert Gunter >> >> "Data is not information. Information is not knowledge. And knowledge >> is certainly not wisdom." >> -- Clifford Stoll >> >> >> On Tue, Sep 22, 2015 at 1:21 PM, John Sorkin >> <JSorkin at grecc.umaryland.edu> wrote: >> > I have data that may be the mixture of two normal distributions (one >> > contained within the other) vs. a single normal. >> > I used normalmixEM to get estimates of parameters assuming two normals: >> > >> > >> > GLUT <- scale(na.omit(data[,"FCW_glut"])) >> > GLUT >> > mixmdl = normalmixEM(GLUT,k=1,arbmean=TRUE) >> > summary(mixmdl) >> > plot(mixmdl,which=2) >> > lines(density(data[,"GLUT"]), lty=2, lwd=2) >> > >> > >> > >> > >> > >> > summary of normalmixEM object: >> > comp 1 comp 2 >> > lambda 0.7035179 0.296482 >> > mu -0.0592302 0.140545 >> > sigma 1.1271620 0.536076 >> > loglik at estimate: -110.8037 >> > >> > >> > >> > I would like to see if the two normal distributions are a better fit >> > that one normal. I have two problems >> > (1) normalmixEM does not seem to what to fit a single normal (even if I >> > address the error message produced): >> > >> > >> >> mixmdl = normalmixEM(GLUT,k=1) >> > Error in normalmix.init(x = x, lambda = lambda, mu = mu, s = sigma, k >> > k, : >> > arbmean and arbvar cannot both be FALSE >> >> mixmdl = normalmixEM(GLUT,k=1,arbmean=TRUE) >> > Error in normalmix.init(x = x, lambda = lambda, mu = mu, s = sigma, k >> > k, : >> > arbmean and arbvar cannot both be FALSE >> > >> > >> > >> > (2) Even if I had the loglik from a single normal, I am not sure how >> > many DFs to use when computing the -2LL ratio test. >> > >> > >> > Any suggestions for comparing the two-normal vs. one normal distribution >> > would be appreciated. >> > >> > >> > Thanks >> > John >> > >> > >> > >> > >> > >> > >> > >> > >> > >> > John David Sorkin M.D., Ph.D. >> > Professor of Medicine >> > Chief, Biostatistics and Informatics >> > University of Maryland School of Medicine Division of Gerontology and >> > Geriatric Medicine >> > Baltimore VA Medical Center >> > 10 North Greene Street >> > GRECC (BT/18/GR) >> > Baltimore, MD 21201-1524 >> > (Phone) 410-605-7119410-605-7119 >> > (Fax) 410-605-7913 (Please call phone number above prior to faxing) >> > >> > >> > Confidentiality Statement: >> > This email message, including any attachments, is for ...{{dropped:12}} >> >> ______________________________________________ >> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide >> http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. > >Call Send SMS Call from mobile Add to Skype You'll need Skype CreditFree via Skype Confidentiality Statement: This email message, including any attachments, is for the sole use of the intended recipient(s) and may contain confidential and privileged information. Any unauthorized use, disclosure or distribution is prohibited. If you are not the intended recipient, please contact the sender by reply email and destroy all copies of the original message.