I am currently in the process of running a meta analysis using the metaSEM package in OpenMx. As you can see in the first pass at the base model I am getting NA values for Std.Error, lbound, ubound, z value and Pr(>|z|) for both Tau2_2 and Tau2_3. In addition, the OpenMx status1: 5, which I found meant "5: means that the Hessian at the solution is not convex." However I am unclear how to resolve this as a problem. In addition when I run models with both level-2 and level-3 constraints I no longer see this issue, but I don't think it would be appropriate to do model comparisons to a base model that has so many NA values. Any help on how to resolve this issue would be great.
Here is the first few lines of data:
AUTHOR YEAR EXP yFINAL vFINAL typeFINAL
Greenwood 2009 I -1.346327273 0.228655603 G
Greenwood 2009 I 0.220196364 0.224990678 G
Siette 2014 J 0.8974913 0.2625858 MT
Siette 2014 J 1.2197971 0.2732485 MT
Siette 2014 J 0.1487526 0.2503457 MT
> t(aggregate(yFINAL~EXP, data=META_B, FUN=length))
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
EXP "I" "J" "K" "L" "M" "N" "R"
yFINAL " 2" " 3" " 2" " 1" "12" " 2" " 1"
> ## ## Model 0: Random-effects model
> summary( Model0 <- meta3(y=yFINAL, v=vFINAL, cluster=EXP,
+ data=META_B, model.name="3 level") )
Call:
meta3(y = yFINAL, v = vFINAL, cluster = EXP, data = META_B, model.name = "3 level")
95% confidence intervals: z statistic approximation
Coefficients:
Estimate Std.Error lbound ubound z value
Intercept 2.8690e-01 2.2100e-01 -1.4626e-01 7.2005e-01 1.2982
Tau2_2 1.0000e-10 NA NA NA NA
Tau2_3 2.6152e-01 NA NA NA NA
Pr(>|z|)
Intercept 0.1942
Tau2_2 NA
Tau2_3 NA
Q statistic on the homogeneity of effect sizes: 38.8583
Degrees of freedom of the Q statistic: 22
P value of the Q statistic: 0.01464862
Heterogeneity indices (based on the estimated Tau2):
Estimate
I2_2 (Typical v: Q statistic) 0.0000
I2_3 (Typical v: Q statistic) 0.5675
Number of studies (or clusters): 7
Number of observed statistics: 23
Number of estimated parameters: 3
Degrees of freedom: 20
-2 log likelihood: 40.06405
OpenMx status1: 5 ("0" or "1": The optimization is considered fine.
Other values may indicate problems.)
> ## ## Model 1: Testing tau^2_3 = 0
> Model1 <- meta3(y=yFINAL, v=vFINAL, cluster=EXP,
+ data=META_B,
+ RE3.constraints=0, model.name="2 level")
Call:
meta3(y = yFINAL, v = vFINAL, cluster = EXP, data = META_B, RE3.constraints = 0,
model.name = "2 level")
95% confidence intervals: z statistic approximation
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
Intercept 0.055543 0.119228 -0.178139 0.289224 0.4659 0.6413
Tau2_2 0.102482 0.113505 -0.119984 0.324948 0.9029 0.3666
Q statistic on the homogeneity of effect sizes: 38.8583
Degrees of freedom of the Q statistic: 22
P value of the Q statistic: 0.01464862
Heterogeneity indices (based on the estimated Tau2):
Estimate
I2_2 (Typical v: Q statistic) 0.3396
I2_3 (Typical v: Q statistic) 0.0000
Number of studies (or clusters): 7
Number of observed statistics: 23
Number of estimated parameters: 2
Degrees of freedom: 21
-2 log likelihood: 45.00194
OpenMx status1: 0 ("0" or "1": The optimization is considered fine.
Other values may indicate problems.)
> Model2 <- meta3(y=yFINAL, v=vFINAL, cluster=EXP,
+ data=META_B,
+ RE2.constraints=0, model.name="tau2_2 EQ 0")
> summary(Model2)
Call:
meta3(y = yFINAL, v = vFINAL, cluster = EXP, data = META_B, RE2.constraints = 0,
model.name = "tau2_2 EQ 0")
95% confidence intervals: z statistic approximation
Coefficients:
Estimate Std.Error lbound ubound z value Pr(>|z|)
Intercept 0.28690 0.25058 -0.20422 0.77801 1.1449 0.2522
Tau2_3 0.26152 0.24783 -0.22423 0.74726 1.0552 0.2913
Q statistic on the homogeneity of effect sizes: 38.8583
Degrees of freedom of the Q statistic: 22
P value of the Q statistic: 0.01464862
Heterogeneity indices (based on the estimated Tau2):
Estimate
I2_2 (Typical v: Q statistic) 0.0000
I2_3 (Typical v: Q statistic) 0.5675
Number of studies (or clusters): 7
Number of observed statistics: 23
Number of estimated parameters: 2
Degrees of freedom: 21
-2 log likelihood: 40.06405
OpenMx status1: 0 ("0" or "1": The optimization is considered fine.
Other values may indicate problems.)