I am trying to perform a GLMM with my simple dataset. I have 2 blocks divided each in 2 plots and in each plot I have my samples units that are trees in this case (5 trees, and for each one I have a specific measurement)). I would like to run a GLMM to see if I got some differences between plots and between blocks and I would like to set the tree as random factor such as : Block(plot(tree)). I got a warning message:

glmm: The final Hessian matrix is not positive definite although all convergence criteria are satisfied. The procedure continues despite this warning. Subsequent results produced are based on the last iteration. Validity of the model fit is uncertain.

When I checked the result, I saw that residual effect do not have result and the parameter is redundant:

**Residual Effect**

Residual Effect Estimate Std. Error Z Sig. 95% Confidence Interval

Lower Upper

Variance ,236a . . . . .

Covariance Structure: Scaled Identity

Subject Specification: (None)

a This parameter is redundant.

Residual Effect Estimate Std. Error Z Sig. 95% Confidence Interval

Lower Upper

Variance ,236a . . . . .

Covariance Structure: Scaled Identity

Subject Specification: (None)

a This parameter is redundant.

If I take out tree as random, everything looks fine. I don't understand why this happened. Could you help me with this issue?

What I did:

**GENLINMIXED**

/DATA_STRUCTURE SUBJECTS=block*plot*tree

/FIELDS TARGET=measurement TRIALS=NONE OFFSET=NONE

/TARGET_OPTIONS DISTRIBUTION=NORMAL LINK=IDENTITY

/FIXED EFFECTS=plot block block*plot USE_INTERCEPT=TRUE

/RANDOM USE_INTERCEPT=TRUE SUBJECTS=block COVARIANCE_TYPE=VARIANCE_COMPONENTS SOLUTION=FALSE

/RANDOM USE_INTERCEPT=TRUE SUBJECTS=block*plot COVARIANCE_TYPE=VARIANCE_COMPONENTS SOLUTION=FALSE

/RANDOM EFFECTS=block(plot(tree)) USE_INTERCEPT=TRUE COVARIANCE_TYPE=VARIANCE_COMPONENTS SOLUTION=FALSE

/BUILD_OPTIONS TARGET_CATEGORY_ORDER=ASCENDING INPUTS_CATEGORY_ORDER=ASCENDING MAX_ITERATIONS=100 CONFIDENCE_LEVEL=95 DF_METHOD=RESIDUAL COVB=MODEL PCONVERGE=0.000001(ABSOLUTE) SCORING=500 SINGULAR=0.000000000001

/EMMEANS_OPTIONS SCALE=ORIGINAL PADJUST=LSD.

/DATA_STRUCTURE SUBJECTS=block*plot*tree

/FIELDS TARGET=measurement TRIALS=NONE OFFSET=NONE

/TARGET_OPTIONS DISTRIBUTION=NORMAL LINK=IDENTITY

/FIXED EFFECTS=plot block block*plot USE_INTERCEPT=TRUE

/RANDOM USE_INTERCEPT=TRUE SUBJECTS=block COVARIANCE_TYPE=VARIANCE_COMPONENTS SOLUTION=FALSE

/RANDOM USE_INTERCEPT=TRUE SUBJECTS=block*plot COVARIANCE_TYPE=VARIANCE_COMPONENTS SOLUTION=FALSE

/RANDOM EFFECTS=block(plot(tree)) USE_INTERCEPT=TRUE COVARIANCE_TYPE=VARIANCE_COMPONENTS SOLUTION=FALSE

/BUILD_OPTIONS TARGET_CATEGORY_ORDER=ASCENDING INPUTS_CATEGORY_ORDER=ASCENDING MAX_ITERATIONS=100 CONFIDENCE_LEVEL=95 DF_METHOD=RESIDUAL COVB=MODEL PCONVERGE=0.000001(ABSOLUTE) SCORING=500 SINGULAR=0.000000000001

/EMMEANS_OPTIONS SCALE=ORIGINAL PADJUST=LSD.

Thank you very much for any help!

Xa