I'm running into an error when using lmer to fit models with no fixed effects terms. For example, generating some data with df$y <- with(df <- data.frame(i = gl(5, 5), b = rep(rnorm(5), each = 5)), b + rnorm(25)) and fitting like this fit1 <- lmer(y ~ 1 + (1 | i), df) works fine. But fitting like this fit0 <- lmer(y ~ 0 + (1 | i), df) gives the following error: CHOLMOD error: Pl? Error in mer_finalize(ans) : Cholmod error `invalid xtype' at file:../Cholesky/cholmod_solve.c, line 971 Am I missing something obvious? Many thanks, Daniel Here's my sessionInfo(), in case it's useful: R version 2.7.1 (2008-06-23) i386-apple-darwin8.10.1 locale: en_GB.UTF-8/en_GB.UTF-8/C/C/en_GB.UTF-8/en_GB.UTF-8 attached base packages: [1] stats graphics grDevices utils datasets methods base other attached packages: [1] lme4_0.999375-26 Matrix_0.999375-15 lattice_0.17-8 loaded via a namespace (and not attached): [1] grid_2.7.1
models with no fixed effects
8 messages · Daniel Farewell, Douglas Bates, Peter Dixon +3 more
On Thu, Sep 11, 2008 at 8:03 AM, Daniel Farewell
<farewelld at cardiff.ac.uk> wrote:
I'm running into an error when using lmer to fit models with no fixed effects terms. For example, generating some data with df$y <- with(df <- data.frame(i = gl(5, 5), b = rep(rnorm(5), each = 5)), b + rnorm(25)) and fitting like this fit1 <- lmer(y ~ 1 + (1 | i), df) works fine. But fitting like this fit0 <- lmer(y ~ 0 + (1 | i), df) gives the following error: CHOLMOD error: Pl? Error in mer_finalize(ans) : Cholmod error `invalid xtype' at file:../Cholesky/cholmod_solve.c, line 971
Admittedly that is a rather obscure error message. It is related to the fact, apparently not verified, that we should have p, the number of fixed-effects, greater than zero. I should definitely add a check on p to the validate method. (In some ways I'm surprised that it got as far as mer_finalize before kicking an error). I suppose that p = 0 could be allowed and I could add some conditional code in the appropriate places but does it really make sense to have p = 0? The random effects are defined to have mean zero. If you have p = 0 that means that E[Y] = 0. I would have difficulty imagining when I would want to make that restriction. Let me make this offer - if someone could suggest circumstances in which such a model would make sense, I will add the appropriate conditional code to allow for p = 0. For the time being I will just add a requirement of p > 0 to the validate method.
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Peter Dixon wrote:
On Sep 11, 2008, at 1:15 PM, Douglas Bates wrote:
I should definitely add a check on p to the validate method. (In some ways I'm surprised that it got as far as mer_finalize before kicking an error). I suppose that p = 0 could be allowed and I could add some conditional code in the appropriate places but does it really make sense to have p = 0? The random effects are defined to have mean zero. If you have p = 0 that means that E[Y] = 0. I would have difficulty imagining when I would want to make that restriction. Let me make this offer - if someone could suggest circumstances in which such a model would make sense, I will add the appropriate conditional code to allow for p = 0. For the time being I will just add a requirement of p > 0 to the validate method.
I think it would make sense to consider a model in which E[Y] = 0 when the data are (either explicitly or implicitly) difference scores. (In fact, I tried to fit such a model with lmer a few months ago and ran into exactly this problem.)
Wouldn't you still need the intercept? The fixed effect tells you whether on average the difference differs from zero. The random effect estimates tell you by how much each individual's difference differs from the mean difference. A
Andy Fugard, Postgraduate Research Student Psychology (Room S6), The University of Edinburgh, 7 George Square, Edinburgh EH8 9JZ, UK +44 (0)78 123 87190 http://figuraleffect.googlepages.com/ The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336.
On Thu, Sep 11, 2008 at 4:09 PM, Peter Dixon <peter.dixon at ualberta.ca> wrote:
I think it would make sense to consider a model in which E[Y] = 0 when the data are (either explicitly or implicitly) difference scores. (In fact, I tried to fit such a model with lmer a few months ago and ran into exactly this problem.)
I had the same initial thoughts, but for me, the intercept tells me how much of the difference remains unexplained by the covariates. Fixing that at 0 is the same as infinitely strong prior belief that there are no other possible explanations for the observed differences. -Aaron
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On 11 Sep 2008, at 22:06, Peter Dixon wrote:
On Sep 11, 2008, at 2:15 PM, Andy Fugard wrote:
Peter Dixon wrote:
On Sep 11, 2008, at 1:15 PM, Douglas Bates wrote:
I should definitely add a check on p to the validate method. (In some ways I'm surprised that it got as far as mer_finalize before kicking an error). I suppose that p = 0 could be allowed and I could add some conditional code in the appropriate places but does it really make sense to have p = 0? The random effects are defined to have mean zero. If you have p = 0 that means that E[Y] = 0. I would have difficulty imagining when I would want to make that restriction. Let me make this offer - if someone could suggest circumstances in which such a model would make sense, I will add the appropriate conditional code to allow for p = 0. For the time being I will just add a requirement of p > 0 to the validate method.
I think it would make sense to consider a model in which E[Y] = 0 when the data are (either explicitly or implicitly) difference scores. (In fact, I tried to fit such a model with lmer a few months ago and ran into exactly this problem.)
Wouldn't you still need the intercept? The fixed effect tells you whether on average the difference differs from zero. The random effect estimates tell you by how much each individual's difference differs from the mean difference. A -- Andy Fugard, Postgraduate Research Student Psychology (Room S6), The University of Edinburgh, 7 George Square, Edinburgh EH8 9JZ, UK +44 (0)78 123 87190 http://figuraleffect.googlepages.com/ The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336.
In the context in which this arose, I was interested in assessing the evidence for an overall positive difference score (i.e., that E(Y)>0), and my strategy was to compare the fit of two models, essentially, D~0+ (1|Subject) and D~1+(1|Subject), using AIC values. To get a sensible assessment of the evidence for the fixed effect, it seemed to me that one would want to have the same random effects in the two models being compared. The second model is clearly more obvious, but the interpretation of D~0+(1|Subject) could be that subjects differ randomly in their response to the treatment, but that there is no consistent effect in the population.
I /think/ I get this, by analogy with how I use AIC/BIC/LRTs to test
predictors. But still a bit confused. The two models are:
y_ij = a + b_j + e_ij (1)
y_ij = c_j + e_ij (2)
Suppose a != 0 in model 1. Then in model 2:
c_j = b_j + a.
(Maybe it's not as simple as this!) But I'm not sure what effect that
would have on the e_ij's - and my intuition says that's what's going
to affect the fit. Also I would have thought model 2 would give a
better fit since having one fewer predictor is going to have less of a
penalising effect in the AIC and BIC.
Andy
The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336.
Not including an intercept term can indeed induce spurious correlation in linear regression, this issue is reviewed in Richard Kronmal's excellent paper Spurious Correlation and the Fallacy of the Ratio Standard Revisited Richard A. Kronmal Journal of the Royal Statistical Society. Series A (Statistics in Society), Vol. 156, No. 3 (1993), pp. 379-392 which could no doubt be readily extended to cover mixed effect models by A Real Statistician. The cost of including an intercept term is small relative to the havoc that can be reaped by not including one. Steven McKinney
-----Original Message----- From: r-sig-mixed-models-bounces at r-project.org on behalf of Andy Fugard Sent: Thu 9/11/2008 3:57 PM To: Peter Dixon Cc: r-sig-mixed-models at r-project.org Subject: Re: [R-sig-ME] models with no fixed effects On 11 Sep 2008, at 22:06, Peter Dixon wrote:
On Sep 11, 2008, at 2:15 PM, Andy Fugard wrote:
Peter Dixon wrote:
On Sep 11, 2008, at 1:15 PM, Douglas Bates wrote:
I should definitely add a check on p to the validate method. (In some ways I'm surprised that it got as far as mer_finalize before kicking an error). I suppose that p = 0 could be allowed and I could add some conditional code in the appropriate places but does it really make sense to have p = 0? The random effects are defined to have mean zero. If you have p = 0 that means that E[Y] = 0. I would have difficulty imagining when I would want to make that restriction. Let me make this offer - if someone could suggest circumstances in which such a model would make sense, I will add the appropriate conditional code to allow for p = 0. For the time being I will just add a requirement of p > 0 to the validate method.
I think it would make sense to consider a model in which E[Y] = 0 when the data are (either explicitly or implicitly) difference scores. (In fact, I tried to fit such a model with lmer a few months ago and ran into exactly this problem.)
Wouldn't you still need the intercept? The fixed effect tells you whether on average the difference differs from zero. The random effect estimates tell you by how much each individual's difference differs from the mean difference. A -- Andy Fugard, Postgraduate Research Student Psychology (Room S6), The University of Edinburgh, 7 George Square, Edinburgh EH8 9JZ, UK +44 (0)78 123 87190 http://figuraleffect.googlepages.com/ The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336.
In the context in which this arose, I was interested in assessing the evidence for an overall positive difference score (i.e., that E(Y)>0), and my strategy was to compare the fit of two models, essentially, D~0+ (1|Subject) and D~1+(1|Subject), using AIC values. To get a sensible assessment of the evidence for the fixed effect, it seemed to me that one would want to have the same random effects in the two models being compared. The second model is clearly more obvious, but the interpretation of D~0+(1|Subject) could be that subjects differ randomly in their response to the treatment, but that there is no consistent effect in the population.
I /think/ I get this, by analogy with how I use AIC/BIC/LRTs to test
predictors. But still a bit confused. The two models are:
y_ij = a + b_j + e_ij (1)
y_ij = c_j + e_ij (2)
Suppose a != 0 in model 1. Then in model 2:
c_j = b_j + a.
(Maybe it's not as simple as this!) But I'm not sure what effect that
would have on the e_ij's - and my intuition says that's what's going
to affect the fit. Also I would have thought model 2 would give a
better fit since having one fewer predictor is going to have less of a
penalising effect in the AIC and BIC.
Andy
--
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.
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