[R] SEM - singularity error
John Fox
jfox at mcmaster.ca
Fri Sep 21 00:46:41 CEST 2007
Dear Nicki,
> -----Original Message-----
> From: nicolette.cagle at duke.edu [mailto:nicolette.cagle at duke.edu]
> Sent: Thursday, September 20, 2007 3:06 PM
> To: John Fox
> Cc: Chuck Cleland; r-help at stat.math.ethz.ch
> Subject: Re: [R] SEM - singularity error
>
> Dear John,
>
> Thank you so much for your assistance, it is greatly
> appreciated. You are correct in your interpretation of the
> variables (Moist and Hab are latent, the other, lower case
> variables are observed). I've attempted to run the model
> again adding Moist <-> Hab (please see code below) and still
> receive the same error message:
>
> "Error in solve.default(C) : system is computationally
> singular: reciprocal condition number = 6.59035e-17."
>
> Is it possible that something is wrong with the
> variance-covariance matrix (please see pasted below r code)?
> Are extremely small values (e.g., 4e-4) problematic? Do you
> have any additional suggestions as to how I might go about
> trouble shooting this problem?
You could set the argument debug=TRUE in the call to sem(), which will give
you more detail about what's going on. But I suspect that the problem is the
very large differences in size among the variances of your observed
variances, differences of many orders of magnitude. You could try the
following: (1) set the argument par.size="start.values"; and, if that
doesn't work, (2) alternatively see what happens when you try to estimate
the model from a correlation rather than a covariance matrix.
>
> I am also attaching the jpeg model diagram, in case it could
> be of use to you.
The diagram is identical to the one that I inferred from your model
specification. I still think that you probably want to allow the two latent
exogenous variables to be correlated.
If neither of these approaches works, then please send me (privately) the
input covariance matrix and model specification as files so that I can take
a closer look.
Regards,
John
>
> Thank you so much for your time.
> Best wishes,
> Nicki
>
> R CODE USED:
> # 20 Sep 2007 SEM of Thamnophis abundance
>
> # LOADING R PACKAGES
> library(sem)
>
> # READING IN THE CSV FILES
> thsi.2006<-read.csv("thsi_ab_env_space_sem.csv")
> thsi<-thsi.2006
>
> # MAKING "RAM" FILE 3
> model3.nlc <-specify.model()
> Moist->slope, NA, 1
> Moist->sand, lamda21, NA
> Moist->clay, lamda31, NA
> Hab->isol, NA, 1
> Hab->edgedist_a, lamda52, NA
> Hab->ag10, lamda62, NA
> Hab->urb10, lamda72, NA
> Hab->rd10, lamda82, NA
> Hab->y, lamda92, NA
> Moist->this, gamma11, NA
> Hab->this, gamma12, NA
> slope<->slope, theta11, NA
> sand<->sand, theta22, NA
> clay<->clay, theta33, NA
> isol<->isol, theta44, NA
> edgedist_a<->edgedist_a, theta55, NA
> ag10<->ag10, theta66, NA
> urb10<->urb10, theta77, NA
> rd10<->rd10, theta88, NA
> y<->y, the99, NA
> Moist<->Moist, phi11, NA
> Hab<->Hab, phi22, NA
> Moist<->Hab, phi21, NA
> this<->this, theps11, NA
>
> model3.nlc
> end
>
> # MAKING S (COVARIANCE MATRIX)
> thsi.var <- var(thsi)
>
> # MAKING UNSCALED SEM MODEL
> sem3<-sem(ram=model3.nlc, S=thsi.var, N=22)
>
> VARIANCE-COVARIANCE MATRIX (AKA: thsi.var):
> this
> this 8.88528139
> edgedist_a 44.91469329
> isol 2678.38321991
> ag10 -0.38967619
> urb10 0.11704827
> rd10 0.02132100
> slope -2.25074394
> clay -36.19339827
> sand 19.66753247
> y -0.95970602
> edgedist_a
> this 44.9146933
> edgedist_a 17491.7873712
> isol 96122.5594957
> ag10 -9.1045614
> urb10 1.9439758
> rd10 0.5333281
> slope 24.4351358
> clay -1360.1102116
> sand 619.1507519
> y -15.4852253
> isol
> this 2678.38322
> edgedist_a 96122.55950
> isol 4167108.48214
> ag10 -347.26757
> urb10 91.79339
> rd10 25.71996
> slope -392.44092
> clay -42236.76039
> sand 19461.19308
> y -868.20597
> ag10
> this -0.38967619
> edgedist_a -9.10456137
> isol -347.26756672
> ag10 0.05167298
> urb10 -0.01314388
> rd10 -0.00297957
> slope 0.06923224
> clay 3.17604271
> sand -1.61043719
> y 0.11896881
> urb10
> this 0.117048268
> edgedist_a 1.943975810
> isol 91.793388529
> ag10 -0.013143880
> urb10 0.003733677
> rd10 0.000784747
> slope -0.039094302
> clay -0.907067141
> sand 0.491619654
> y -0.034343332
> rd10
> this 0.0213209957
> edgedist_a 0.5333280831
> isol 25.7199633947
> ag10 -0.0029795700
> urb10 0.0007847471
> rd10 0.0001987203
> slope -0.0041496227
> clay -0.2726142316
> sand 0.1286087229
> y -0.0078502982
> slope
> this -2.250744e+00
> edgedist_a 2.443514e+01
> isol -3.924409e+02
> ag10 6.923224e-02
> urb10 -3.909430e-02
> rd10 -4.149623e-03
> slope 2.520968e+00
> clay 3.343637e+00
> sand -2.202094e+00
> y 3.306712e-01
> clay
> this -3.619340e+01
> edgedist_a -1.360110e+03
> isol -4.223676e+04
> ag10 3.176043e+00
> urb10 -9.070671e-01
> rd10 -2.726142e-01
> slope 3.343637e+00
> clay 7.962072e+02
> sand -3.410372e+02
> y 1.096320e+01
> sand
> this 19.6675325
> edgedist_a 619.1507519
> isol 19461.1930766
> ag10 -1.6104372
> urb10 0.4916197
> rd10 0.1286087
> slope -2.2020936
> clay -341.0372225
> sand 165.1578113
> y -5.4148540
> y
> this -9.597060e-01
> edgedist_a -1.548523e+01
> isol -8.682060e+02
> ag10 1.189688e-01
> urb10 -3.434333e-02
> rd10 -7.850298e-03
> slope 3.306712e-01
> clay 1.096320e+01
> sand -5.414854e+00
> y 3.694397e-01
>
>
> Quoting John Fox <jfox at mcmaster.ca>:
>
> > Dear Nicolette and Chuck,
> >
> > I apologize for not seeing Nicolette's original posting.
> >
> > The model does appear to be correctly specified (though I
> didn't see
> > the path diagram) and over-identified. I assume that all of the
> > variables with lower-case names are observed variables and
> that "Moist"
> > and "Hab" are latent variables. (Simply comparing the
> number of free
> > parameters to the number of unique covariances among observed
> > variables provides a necessary but not sufficient condition
> for identification.
> > This model is identified because there more than two unique
> indicators
> > for each latent variable and because the structural
> submodel relating
> > "this" to "Moist" and "Hab" is identified.)
> >
> > I suspect that the problem here is the restriction that "Moist" and
> > "Hab" are uncorrelated, which follows from the lack of a
> double-headed
> > arrow connecting these variables. You might try adding
> Moist <-> Hab
> > to the model.
> >
> > I hope this helps,
> > John
> >
> >
> > On Thu, 20 Sep 2007 12:40:06 -0400
> > Chuck Cleland <ccleland at optonline.net> wrote:
> >> nicolette.cagle at duke.edu wrote:
> >> > Good morning,
> >> >
> >> > I am trying to develop a structural equation model of snake
> >> abundance using
> >> > habitat variables. In attempting to estimate the model using the
> >> "sem" package
> >> > in R version 2.4.0, I receive the following error message:
> >> >
> >> > "Error in solve.default(C) : system is computationally singular:
> >> reciprocal
> >> > condition number = 1.75349e-16"
> >> >
> >> > MAIN PROBLEM: I am hoping to discover why I am receiving the
> >> aforementioned
> >> > error message and how to successfully estimate the model.
> >> >
> >> > OTHER INFORMATION:
> >> > 1. I believe the model is over-identified rather than
> >> under-identified (based on
> >> > my understanding of the t-rule). I have observed data for 10
> >> variables (9
> >> > exogenous, 1 endogenous).
> >> >
> >> > 2. I am not certain that I have used the proper tool to estimate
> >> the covariance
> >> > matrix. In this case, I used the "VAR" function.
> >> >
> >> > 3. I am most concerned that I have improperly coded the RAM file.
> >> For example,
> >> > in a case where I have three exogenous indicators of one
> exogenous
> >> latent
> >> > variable, I specify a start value of 1 for one of the exogenous
> >> indicators. I
> >> > am not sure if this is proper or necessary.
> >> >
> >> > 4. I am new to SEM; this is the first model I have ever tried to
> >> estimate.
> >> >
> >> > R CODE: Below is the r-code I have used to estimate the
> structural
> >> equation
> >> > model --
> >> >
> >> > # LOADING R PACKAGES
> >> > library(sem)
> >> >
> >> > # READING IN THE CSV FILES
> >> > thsi.2006<-read.csv("thsi_ab_env_space_sem.csv")
> >> > thsi<-thsi.2006
> >> >
> >> > # MAKING "RAM" FILE 2
> >> > model2.nlc <-specify.model()
> >> > Moist->slope, NA, 1
> >> > Moist->sand, lamda21, NA
> >> > Moist->clay, lamda31, NA
> >> > Hab->isol, NA, 1
> >> > Hab->edgedist_a, lamda52, NA
> >> > Hab->ag10, lamda62, NA
> >> > Hab->urb10, lamda72, NA
> >> > Hab->rd10, lamda82, NA
> >> > Hab->y, lamda92, NA
> >> > Moist->this, gamma11, NA
> >> > Hab->this, gamma12, NA
> >> > slope<->slope, theta11, NA
> >> > sand<->sand, theta22, NA
> >> > clay<->clay, theta33, NA
> >> > isol<->isol, theta44, NA
> >> > edgedist_a<->edgedist_a, theta55, NA ag10<->ag10, theta66, NA
> >> > urb10<->urb10, theta77, NA rd10<->rd10, theta88, NA
> y<->y, the99,
> >> > NA Moist<->Moist, phi11, NA Hab<->Hab, phi22, NA this<->this,
> >> > theps11, NA
> >> >
> >> > model2.nlc
> >> > end
> >> >
> >> > # MAKING S (COVARIANCE MATRIX)
> >> > thsi.var <- var(thsi)
> >> >
> >> > # MAKING UNSCALED SEM MODEL
> >> > sem2<-sem(ram=model2.nlc, S=thsi.var, N=22)
> >> >
> >> > I am also attaching a jpeg diagram of the model I am trying to
> >> estimate. Please
> >> > let me know if there is any additional information that I should
> >> add to this
> >> > posting.
> >> >
> >> > Thank you so much for your time.
> >> > Nicolette Cagle
> >>
> >> Your specification of the model seems OK and it is
> over-identified
> >> (21
> >> free parameters and 34 df). I suspect the problem is that one or
> >> more of your 10 variables is a linear function of the remaining
> >> variables.
> >> If that is the case, then the following should give the same
> >> singularity
> >> error:
> >>
> >> factanal(thsi, factors=1)
> >>
> >> You may be able to drop one or more of the 10 variables from
> >> consideration and successfully estimate a conceptually
> similar model.
> >>
> >> hope this helps,
> >>
> >> Chuck Cleland
> >>
> >> >
> >>
> >
> ----------------------------------------------------------------------
> > --
> >> >
> >> > ______________________________________________
> >> > R-help at r-project.org mailing list
> >> > 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.
> >>
> >> --
> >> Chuck Cleland, Ph.D.
> >> NDRI, Inc.
> >> 71 West 23rd Street, 8th floor
> >> New York, NY 10010
> >> tel: (212) 845-4495 (Tu, Th)
> >> tel: (732) 512-0171 (M, W, F)
> >> fax: (917) 438-0894
> >>
> >> ______________________________________________
> >> R-help at r-project.org mailing list
> >> 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.
> >
> > --------------------------------
> > John Fox, Professor
> > Department of Sociology
> > McMaster University
> > Hamilton, Ontario, Canada
> > http://socserv.mcmaster.ca/jfox/
> >
>
>
>
> --
> Ecology Ph.D. Candidate
> Duke University
> Durham, NC 27708
> www.duke.edu/~nlc4
>
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