lavaan ERROR: initial model-implied matrix (Sigma) is not positive definite;

[Siu Lam]

Hi, I'm working on a univariate latent change score model using the Lavaan package. It has two-time points. When I tried to fix the variance of the change scores at 0, it gave me an error 

Error in lav_model_estimate(lavmodel = lavmodel, lavsamplestats = lavsamplestats,  : 

  lavaan ERROR: initial model-implied matrix (Sigma) is not positive definite;

  check your model and/or starting parameters.

I then tried to modify it by using the starting value at 0.001. Then the error is gone. I wonder why is that?  Following is the code. 

Model<-'

T2 ~ 1*T1     # Fixed regression of T2 on T1

dT =~ 1*T2     # Fixed regression of dT on T2

T2 ~ 0*1          # This line constrains the intercept of T2 to 0

T2 ~~ 0*T2    # This fixes the variance of the T2 to 0 

dT ~ 1             # This estimates the intercept of the change scores 

T1 ~  1           # This estimates the intercept of T1 

dT1 ~~  dT1       # This estimates the variance of the change scores (It doesn't work if I fix it at 0. However, it does work if I fix it at 0.001.)

T1 ~~   T1    # This estimates the variance of T1 

dT ~ T1          # This estimates the self-feedback parameter

'

fit <- lavaan(Model, data=Data1, estimator='mlr',fixed.x=FALSE,missing='fiml')

summary(fitULCS, fit.measures=TRUE, standardized=TRUE, rsquare=TRUE)

Thank you for reading. 

[Terrence Jorgensen]

When I tried to fix the variance of the change scores at 0, it gave me an error 

Assuming there is nothing else wrong with your model specification, the lavaan() function does not always give smart starting values if it cannot guess what they should be from your model specification, leading to the error you see.  You can try using the sem() function, or changing some of lavaan's default arguments:

?lavOptions

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

UvA web page: http://www.uva.nl/profile/t.d.jorgensen

[Siu Lam]

Thank you for the suggestion! 

[John Mathews]

I m trying to stimulate a 4-Likert cat dataset i receive this error when I m adding the thresholds statements 

population.model="

! regressions 

   SE=~0.7*x1+0.7*x2+0.7*x3+0.7*x4+0.7*x5+0.7*x6+0.7*x7+0.7*x8

   ET=~0.7*x9+0.7*x10+0.7*x11+0.7*x12+0.7*x13

  

   RI=~0.7*y1+0.7*y2+0.7*y3+0.7*y4+0.7*y5+0.7*y6+0.7*y7

   PG=~0.7*y8+0.7*y9+0.7*y10+0.7*y11+0.7*y12+0.7*y13+0.7*y14+0.7*y15+0.7*y16+0.7*y17

   

   SE=~RI

   ET=~RI

   RI=~PG

   SE=~PG

   ET=~PG

! residuals, variances and covariances

   SE ~~ 0.51*SE

   ET ~~ 0.51*ET

   SE ~~ 0.25*ET

   RI ~~ 0.51*RI

   x1 ~~ 0.51*x1

    x2 ~~ 0.51*x2

   x3 ~~ 0.51*x3

   x4 ~~ 0.51*x4

   x5 ~~ 0.51*x5

   x6 ~~ 0.51*x6

   x7 ~~ 0.51*x7

   x8 ~~ 0.51*x8

  x9 ~~ 0.51*x9

x10 ~~ 0.51*x10

   x11 ~~ 0.51*x11

   x12 ~~ 0.51*x12

   x13 ~~ 0.51*x13

   

   y1 ~~ 0.51*y1

   y2 ~~ 0.51*y2

   y3 ~~ 0.51*y3

   y4 ~~ 0.51*y4

   y5 ~~ 0.51*y5

   y6 ~~ 0.51*y6

   y7 ~~ 0.51*y7

   PG ~~ 0.51*PG

   y8 ~~ 0.51*y8

   y9 ~~ 0.51*y9

   y10 ~~ 0.51*y10

   y11 ~~ 0.51*y11

   y12 ~~ 0.51*y12

   y13 ~~ 0.51*y13

   y14 ~~ 0.51*y14

   y15 ~~ 0.51*y15

   y16 ~~ 0.51*y16

   y17 ~~ 0.51*y17

! means

  ET+RI+PG+ SE~1*1;

  x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12+x13~1*1;

  y1+y2+y3+y4+y5+y6+y7+y8+y9+y10+y11+y12+y13+y14+y15+y16+y17~1*1; 

  x1 ~*~ x1

x2 ~*~ x2

x3 ~*~ x3

x4 ~*~ x4

x5 ~*~ x5

x7 ~*~ x7

x8 ~*~ x8

x9 ~*~ x9

x10 ~*~ x10

x11 ~*~ x11

x12 ~*~ x12

x13 ~*~ x13

x1 | -.1*t1 + 0.8*t2+1.5*t3

x2 | -.1*t1 + 0.8*t2+1.5*t3

x3 | -.1*t1 + 0.8*t2+1.5*t3

x4 | -.1*t1 + 0.8*t2+1.5*t3

x5 | -.1*t1 + 0.8*t2+1.5*t3

x6 | -.1*t1 + 0.8*t2+1.5*t3

x7 | -.1*t1 + 0.8*t2+1.5*t3

x8 | -.1*t1 + 0.8*t2+1.5*t3

x9 | -.1*t1 + 0.8*t2+1.5*t3

x10 | -.1*t1 + 0.8*t2+1.5*t3

x11 | -.1*t1 + 0.8*t2+1.5*t3

x12 | -.1*t1 + 0.8*t2+1.5*t3

x13 | -.1*t1 + 0.8*t2+1.5*t3

y1 ~*~ y1

y2 ~*~ y2

y3 ~*~ y3

y4 ~*~ y4

y5 ~*~ y5

y7 ~*~ y7

y8 ~*~ y8

y9 ~*~ y9

y10 ~*~ y10

y11 ~*~ y11

y12 ~*~ y12

y13 ~*~ y13

y14 ~*~ y14

y15 ~*~ y15

y16 ~*~ y16

y17 ~*~ y17

y1 | -.1*t1 + 0.8*t2+1.5*t3

y2 | -.1*t1 + 0.8*t2+1.5*t3

y3 | -.1*t1 + 0.8*t2+1.5*t3

y4 | -.1*t1 + 0.8*t2+1.5*t3

y5 | -.1*t1 + 0.8*t2+1.5*t3

y6 | -.1*t1 + 0.8*t2+1.5*t3

y7 | -.1*t1 + 0.8*t2+1.5*t3

y8 | -.1*t1 + 0.8*t2+1.5*t3

y9 | -.1*t1 + 0.8*t2+1.5*t3

y10 | -.1*t1 + 0.8*t2+1.5*t3

y11 | -.1*t1 + 0.8*t2+1.5*t3

y12 | -.1*t1 + 0.8*t2+1.5*t3

y13 | -.1*t1 + 0.8*t2+1.5*t3

y14 | -.1*t1 + 0.8*t2+1.5*t3

y15 | -.1*t1 + 0.8*t2+1.5*t3

y16 | -.1*t1 + 0.8*t2+1.5*t3

y17 | -.1*t1 + 0.8*t2+1.5*t3 

";

dat.sim = simulateData(population.model, sample.nobs=50,skewness =1,kurtosis = 3.5, seed = 2020)

 can someone help me 

[Edward Rigdon]

Did you mean here:

  SE=~RI

   ET=~RI

   RI=~PG

   SE=~PG

   ET=~PG

that each of these factors is somehow a higher order factor of the other factors? That is what the =~ operator is telling lavaan. Did you just mean a regression relation, where the operator is just ~ ?

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[John Mathews]

higher order factor of the other factors  

[Terrence Jorgensen]

I m trying to stimulate a 4-Likert cat dataset i receive this error when I m adding the thresholds statements 

Not sure if this is the reason for the error, but why are you specifying both residual variances AND scaling factors (with the ~*~ operator)?  One implies the other.  I would omit the scaling factors (which don't have population values anyway) and just leave your residual variances in there (which do have population values).  And perhaps you would have to set parameterization = "theta" too?

   SE=~RI

   ET=~RI

   RI=~PG

   SE=~PG

   ET=~PG

Is there a reason you are thinking of RI & PG as indicators of SE and ET (and RI)?  All of those factors have observed indicators.  Second-order loadings are just in the Beta matrix, and it is arbitrary to just define the regression paths instead.  Try doing this, in case that is throwing lavaan's expectations off:

RI ~ SE + ET

PG ~ RI + SE + ET

But remember to specify population values for those slopes, don't just leave the parameters "blank".

! means

  ET+RI+PG+ SE~1*1;

  x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12+x13~1*1;

  y1+y2+y3+y4+y5+y6+y7+y8+y9+y10+y11+y12+y13+y14+y15+y16+y17~1*1; 

Do you realize you are setting your latent means to 1 instead of 0?  There's nothing actually wrong with that, but you would not be able to recover the other population parameters because the intercepts of latent item-responses are fixed to zero for identification when estimating the model.

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[José Antonio Moreira de Rezende]

I received this error when I was trying to solve the following model (V2 and V14 was excluded because of std = 0):

model <- '
  # measurement model
  F1 =~ V8 + V9
  F2 =~ V10 + V11 + V12 + V16 + V17 + V18 + V19 + V20 + V21 + V22
  F3 =~ V13

  # regressions
  V3 ~ V4
  V7 ~ V1 + F1
  V8 ~ F1
  V9 ~ F1
  V10 ~ F2
  V11 ~ F2
  V12 ~ F2
  V16 ~ F2
  V17 ~ F2
  V18 ~ F2
  V19 ~ F2
  V20 ~ F2
  V21 ~ F2
  V22 ~ F2
  V13 ~ F3
  V15 ~ V6 + V7 + F1
  F1 ~ V1 + V3 + V4
  F2 ~ V5
  F3 ~ V5

  # variances
  F2 ~~ F3
  V8 ~~ V9
  V15 ~~ F3
  V15 ~~ F2
'

I normalized and scaled the input values (in the attachment). It gave me the errors:

1: lavaan->lav_model_estimate():  

   initial model-implied matrix (Sigma) is not positive definite; check your model and/or starting parameters .

2: lavaan->lav_model_estimate():  

   initial model-implied matrix (Sigma) is not positive definite; check your model and/or starting parameters .

3: lavaan->lav_model_estimate():  

   initial model-implied matrix (Sigma) is not positive definite; check your model and/or starting parameters .

4: lavaan->lav_model_estimate():  

   initial model-implied matrix (Sigma) is not positive definite; check your model and/or starting parameters .

5: lavaan->lav_lavaan_step11_estoptim():  
   Model estimation FAILED! Returning starting values. 

[José Antonio Moreira de Rezende]

Sorry, I think I forgot to attach the file.

[José Antonio Moreira de Rezende]

Hello, everyone.

Since no one has responded to my question so far, I believe I may not have been specific enough to provide a clear understanding of the problem. I am available to provide further clarification if needed.

The data used in my analysis comes from the 2010 demographic census conducted by IBGE, the Brazilian agency responsible for that year’s census survey. The data of interest is associated with a specific municipality in the state of Minas Gerais (Brazil), and my research aims to explore causal relationships within families whose per capita household income is up to half the minimum wage.

To create a dataset suitable for use with the lavaan package, the data was sourced from two files. The first file contains census information about households, and the second includes data about individuals surveyed. The CSV file I shared is the result of a probabilistic match, where each individual was randomly assigned to a household within the same income category. The resulting data was then adjusted to a normal distribution and scaled to have a mean of zero and a variance of one.

Thus, the CSV file contains both continuous, binary and categorical data. The categorical variables were adjusted following the approach detailed by Bollen (2014) in Chapter 9 (reference in the end of this message). As mentioned in my message from november 28th, variables V2 and V14 were excluded from the model because they resulted in zero variance during the data filtering process. Rows with missing data were also discarded.

Below is the description of each observable and latent variable:

• V1: Age (integer)
• V3: Highest level of academic education (categorical: 1 to 14)
• V4: Ethnical (categorical: 1, 2, 3, 4, 5, 9)
• V5: Household in urban or rural area (binary: 1, 2)
• V6: Lives with a spouse or partner (categorical: 1, 2, 3)
• V7: Total number of living children as of July 31, 2010 (integer)
• V8: Employment status (categorical: 1 to 7)
• V9: Was contributing to an official social security institution for any job held during the week of July 25–31, 2010 (categorical: 1, 2, 3)
• V10: Presence of a refrigerator in the household (binary: 1, 2)
• V11: Presence of a television in the household (binary: 1, 2)
• V12: Number of bathrooms in the household (integer: 0 to 9)
• V13: Source of water supply in the household (categorical: 1 to 10)
• V15: Monthly per capita income in terms of minimum wages (real number)
• V16: Presence of an electricity meter in the household (categorical: 1, 2, 3)
• V17: Presence of a radio (binary: 1, 2)
• V18: Presence of a washing machine (binary: 1, 2)
• V19: Presence of a mobile phone (binary: 1, 2)
• V20: Presence of a landline phone (binary: 1, 2)
• V21: Presence of a computer (binary: 1, 2)
• V22: Presence of a computer with internet access (binary: 1, 2)

The reference of Bollen (2014) is: Bollen, K. A. (2014). Structural Equations with Latent Variables. Wiley.

I hope this additional information helps clarify my query, and I am available to discuss any aspect of the dataset or model further. Thank you in advance for your assistance and have a nice weekend.

Best regards!