Multivariate Latent Growth Curve Model

[René Britschgi]

Dear Lavaan users,

I`m trying to set up a multivariate latent growth curve model consisting out of three latent growth curve models. In particular I`m interested whether and how outcome (io = intercept of outcome orientation, so = slope of outcome orientation) and process orientation (ip = intercept of outcome orientation, sp = slope of process orientation) relate to boredom (i = intercept of boredom, s = slope of boredom) over the course of ca. 30 minutes (4 measurements). First I tried a multivariate growth curve model with boredom and process orientation. That worked and I could see how the intercepts and slopes of these two models are related to each other. Then I looked at boredom and outcome orientation. This also worked. However, when I include all three growth curve models I get the following warning messages:  

Warning messages:

1: In lavaan::lavaan(model = growth1, data = Recoded, estimator = "mlr",  :

  lavaan WARNING: some estimated variances are negative

2: In lavaan::lavaan(model = growth1, data = Recoded, estimator = "mlr",  :

  lavaan WARNING: covariance matrix of latent variables is not positive definite; use inspect(fit,"cov.lv") to investigate.

I`m not really familiar with the math behind this. So I`m wondering whether there is a way to fix these problems or is the model just too complex?

I`m looking forward to your responses and comments.

Thanks in advance,

René

> growth1 <- 'i =~ 1*B_2nd_r + 1*B_3rd_r + 1*B_4th_r + 1*B_5th_r

+ s =~ 0*B_2nd_r + 1*B_3rd_r + 2*B_4th_r + 3*B_5th_r

+ 

+ ip =~ 1*GF01_06 + 1*GF02_06 + 1*GF03_06 + 1*GF04_06

+ sp =~ 0*GF01_06 + 1*GF02_06 + 2*GF03_06 + 3*GF04_06

+ 

+ io =~ 1*O1_r + 1*O2_r + 1*O3_r + 1*O4_r

+ so =~ 0*O1_r + 1*O2_r + 2*O3_r + 3*O4_r

+ 

+ i ~ ip + sp + io + so

+ s ~ ip + sp + io + so 

+ 

+ 

+ '

> 

> 

> fit <- growth (model = growth1, estimator="mlr", data=Recoded)

Warning messages:

1: In lavaan::lavaan(model = growth1, data = Recoded, estimator = "mlr",  :

  lavaan WARNING: some estimated variances are negative

2: In lavaan::lavaan(model = growth1, data = Recoded, estimator = "mlr",  :

  lavaan WARNING: covariance matrix of latent variables is not positive definite; use inspect(fit,"cov.lv") to investigate.

> summary(fit, fit.measures = TRUE)

lavaan (0.5-16) converged normally after 8687 iterations

  Number of observations                           131

  Estimator                                         ML      Robust

  Minimum Function Test Statistic               84.770      77.002

  Degrees of freedom                                51          51

  P-value (Chi-square)                           0.002       0.011

  Scaling correction factor                                  1.101

    for the Yuan-Bentler correction

Model test baseline model:

  Minimum Function Test Statistic             1471.567    1066.447

  Degrees of freedom                                66          66

  P-value                                        0.000       0.000

User model versus baseline model:

  Comparative Fit Index (CFI)                    0.976       0.974

  Tucker-Lewis Index (TLI)                       0.969       0.966

Loglikelihood and Information Criteria:

  Loglikelihood user model (H0)              -7156.235   -7156.235

  Scaling correction factor                                  1.312

    for the MLR correction

  Loglikelihood unrestricted model (H1)      -7113.850   -7113.850

  Scaling correction factor                                  1.192

    for the MLR correction

  Number of free parameters                         39          39

  Akaike (AIC)                               14390.470   14390.470

  Bayesian (BIC)                             14502.603   14502.603

  Sample-size adjusted Bayesian (BIC)        14379.250   14379.250

Root Mean Square Error of Approximation:

  RMSEA                                          0.071       0.062

  90 Percent Confidence Interval          0.043  0.097       0.032  0.088

  P-value RMSEA <= 0.05                          0.100       0.218

Standardized Root Mean Square Residual:

  SRMR                                           0.048       0.048

Parameter estimates:

  Information                                 Observed

  Standard Errors                   Robust.huber.white

                   Estimate  Std.err  Z-value  P(>|z|)

Latent variables:

  i =~

    B_2nd_r           1.000

    B_3rd_r           1.000

    B_4th_r           1.000

    B_5th_r           1.000

  s =~

    B_2nd_r           0.000

    B_3rd_r           1.000

    B_4th_r           2.000

    B_5th_r           3.000

  ip =~

    GF01_06           1.000

    GF02_06           1.000

    GF03_06           1.000

    GF04_06           1.000

  sp =~

    GF01_06           0.000

    GF02_06           1.000

    GF03_06           2.000

    GF04_06           3.000

  io =~

    O1_r              1.000

    O2_r              1.000

    O3_r              1.000

    O4_r              1.000

  so =~

    O1_r              0.000

    O2_r              1.000

    O3_r              2.000

    O4_r              3.000

Regressions:

  i ~

    ip               -3.759    1.724   -2.181    0.029

    sp               34.158   11.077    3.084    0.002

    io               -0.502    1.198   -0.419    0.675

    so              -19.495   10.358   -1.882    0.060

  s ~

    ip                1.283    0.945    1.358    0.174

    sp              -13.057    8.497   -1.537    0.124

    io                0.174    0.503    0.345    0.730

    so                6.702    4.692    1.428    0.153

Covariances:

  ip ~~

    sp               61.629   24.247    2.542    0.011

    io              257.678   91.725    2.809    0.005

    so               -0.485   26.362   -0.018    0.985

  sp ~~

    io               14.547   32.645    0.446    0.656

    so               36.870   10.586    3.483    0.000

  io ~~

    so              -49.448   44.064   -1.122    0.262

  i ~~

    s               618.880  335.534    1.844    0.065

Intercepts:

    B_2nd_r           0.000

    B_3rd_r           0.000

    B_4th_r           0.000

    B_5th_r           0.000

    GF01_06           0.000

    GF02_06           0.000

    GF03_06           0.000

    GF04_06           0.000

    O1_r              0.000

    O2_r              0.000

    O3_r              0.000

    O4_r              0.000

    i               434.183  162.034    2.680    0.007

    s              -134.360  109.335   -1.229    0.219

    ip               67.110    2.620   25.613    0.000

    sp               -4.226    0.940   -4.498    0.000

    io               55.128    3.193   17.264    0.000

    so               -1.434    0.916   -1.565    0.118

Variances:

    B_2nd_r         261.902   97.496

    B_3rd_r         250.842   55.155

    B_4th_r         224.109   49.851

    B_5th_r         189.998   75.283

    GF01_06         452.438   98.061

    GF02_06         154.638   45.688

    GF03_06         237.029   66.348

    GF04_06         321.221   75.863

    O1_r            459.608  110.295

    O2_r            212.102   67.912

    O3_r             89.950   29.050

    O4_r             86.396   54.248

    i             -1070.086 1029.194

    s              -203.109  216.301

    ip              633.878  102.862

    sp               27.450   11.025

    io             1110.082  119.542

    so               69.215   22.549

[yrosseel]

On 06/03/2014 06:21 PM, René Britschgi wrote:
> Warning messages:
> 1: In lavaan::lavaan(model = growth1, data = Recoded, estimator = "mlr", :
> lavaan WARNING: some estimated variances are negative

This one is serious. You have negative variances, which is (often) a
symptom of model misfit. I would start with a more simple model, and
gradually add more components, so you can see at which point you get the
negative variances.

I also notices that some regression coefficients and (residual)
variances were fairly large. Perhaps you need to consider rescaling your
data, so that most observed variables are more or less on the same
scale. (say, between 0 and 10).

Yves.

[René Britschgi]

Thank you Yves. 

Yes, maybe it`s better to use factor scores for further analysis. 

Best, 

René