Dear all,
I'm  a PhD student in Cognitive science. I'm working on an analysis with mixed models with R (lme4 and lmerTest)  but I'm  still in trouble with random factors.
I have read some Baayen's works and I tried to follow his methods, but every time, after comparing models with different slopes, the output of lmer is the summary of the model preceded by:

"Asymptotic covariance matrix A is not positive!"

I want to ask you what kind of problems can I have with this message and, most of all, I'm writing to you to ask if you can advise me a shared procedure for random structure.

I have this kind of models: with 3way interaction or 2way interaction.

lex0 = lmer(rt~Trial +first_letter+letters+w.pw*group*manipulation+ (1|Sj)+ (1|Word),lex)

the main thing is to see if there is an interaction between groups and manipulation.  The other fixed factors are predictors



Random effects:

 Groups   Name        Variance Std.Dev.

 Word     (Intercept) 0.006321 0.0795

 Sj       (Intercept) 0.022424 0.1497

 Residual             0.032240 0.1796

Number of obs: 7169, groups: Word, 240; Sj, 32



Fixed effects:

                              Estimate Std. Error         df t value Pr(>|t|)

(Intercept)                  6.554e+00  6.565e-02  1.910e+02  99.839  < 2e-16 ***

Trial                       -7.969e-05  8.026e-06  6.944e+03  -9.930  < 2e-16 ***

first_letterR               -6.763e-03  1.279e-02  2.210e+02  -0.529   0.5976

letters                      1.715e-02  7.378e-03  2.210e+02   2.325   0.0210 *

w.pwW                       -1.562e-01  2.717e-02  3.020e+02  -5.750 2.19e-08 ***

groupnon_expert             -2.182e-02  5.489e-02  3.400e+01  -0.398   0.6934

manipulation                -4.951e-04  3.486e-04  3.190e+02  -1.420   0.1566

w.pwW:groupnon_expert        4.818e-02  1.979e-02  6.884e+03   2.434   0.0150 *

w.pwW:manipulation           5.698e-04  4.936e-04  3.080e+02   1.154   0.2493

groupnon_expert:manipulation 6.275e-04  2.567e-04  6.884e+03   2.444   0.0146 *

w.pwW:groupnon_expert:manipulation -6.664e-04  3.607e-04  6.884e+03  -1.847   0.0647 .

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How can I adjust my random structure?
Thanks,
Tania


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