[R-meta] I2 stats with NA values

[Martineau, Roger]

Hi Metafor users,

I have a data set with missing values for ArgMean:

> tmp.dat.Arg3$ArgMean
  [1]     NA     NA  53.00  58.50     NA     NA     NA     NA
  [9]     NA     NA     NA  76.40  71.70  85.70  84.10  61.90
[17]  62.20 153.00 153.00 144.00 143.00  63.00  60.00  58.50
[25]  60.70  80.60  92.30  67.39  68.66  87.49  78.42  71.30
[33]  69.12  71.30  69.80  68.60  79.22     NA     NA  83.00
[41]  97.00 117.00 115.00  83.00  95.00 115.00 106.00  75.77
[49]  74.05  74.05  84.96  91.85 102.18  98.70  86.30  98.90
[57]  87.20  53.70  80.00  53.70  80.30     NA     NA  59.00
[65]  61.00  47.00  53.00 100.40 103.30 111.40  89.20 102.70
[73]     NA     NA  61.50  60.50  54.40  69.10  68.30  63.80
[81] 111.00 107.00 113.00 109.00  59.80  84.50  57.40  83.80
[89]  56.00  63.00  71.00  68.00  56.00  64.00  70.00  67.00
[97]  82.40  82.80  94.20     NA     NA     NA  77.50  80.94
[105]  78.80 110.30  73.00  97.60  73.00  77.70  63.00  63.00
[113]  77.00  87.00  63.00  62.00  76.00  80.00  65.90  62.57
[121]  68.00  79.00  60.00  72.00  67.00  71.00


My 4-level model using rma.mv function is:


> (tmp.CD <- rma.mv(ArgMean, ArgSEMtrDP^2, data=tmp.dat.Arg3,

+                    mods = ~

+                      cArgDI +

+                      factor(Breed) +

+                      factor(Breed)*cArgDI +

+                      factor(Stage) +

+                      factor(Stage)*cArgDI +

+                      factor(CD) +

+                      factor(CD)*cArgDI,

+                    random = ~1|laboratory/experiment/study,

+                    method = "REML"))

The model is solved with the rma.mv function and indeed I get a warning message:

Warning message:

In rma.mv(ArgMean, ArgSEMtrDP^2, data = tmp.dat.Arg3, mods = ~cArgDI +  :

  Rows with NAs omitted from model fitting.

Cook’s distance and robust functions work fine.

Upon calculation of I^2 statistic, I get the following:

> # Calculation of I^2 statistic
> W <- diag(1/tmp.dat.Arg3$ArgSEMtrDP^2)
> X <- model.matrix(tmp.CD)
> P <- W - W %*% X %*% solve(t(X) %*% W %*% X) %*% t(X) %*% W
Error in W %*% X : non-conformable arguments
> 100 * sum(tmp.CD$sigma2) /
+   (sum(tmp.CD$sigma2) + (tmp.CD$k-tmp.CD$p)/sum(diag(P)))
Error in diag(P) : object 'P' not found

> # Separation of total variance by cluster
> 100 * tmp.CD$sigma2 / (sum(tmp.CD$sigma2) + (tmp.CD$k-tmp.CD$p)/sum(diag(P)))
Error in diag(P) : object 'P' not found


>



If I remove NA values for ArgMean, then I can solve I^2 statistic:

> tmp.dat.Arg3 <- subset (tmp.dat.Arg3,ArgMean > 0)


> # Calculation of I^2 statistic
> W <- diag(1/tmp.dat.Arg3$ArgSEMtrDP^2)
> X <- model.matrix(tmp.CD)
> P <- W - W %*% X %*% solve(t(X) %*% W %*% X) %*% t(X) %*% W
> 100 * sum(tmp.CD$sigma2) /
+   (sum(tmp.CD$sigma2) + (tmp.CD$k-tmp.CD$p)/sum(diag(P)))
[1] 93.233

> # Separation of total variance by cluster
> 100 * tmp.CD$sigma2 / (sum(tmp.CD$sigma2) + (tmp.CD$k-tmp.CD$p)/sum(diag(P)))
[1]  0.0000022494 90.8175748834  2.4158304680


>



Is it possible to get I^2 statistic directly without removing NA values?

The residual heterogeneity is very high and it might be normal given the data analyzed ??. It is a meta-analysis on 108 raw treatment means from 44 studies, clustered within 29 experiments, themselves clustered within 16 laboratories. The effect of factor CD (type of studies) on the relationship was NS and is shown below:


[cid:image001.jpg at 01D31106.A455D1C0]



Best,

Roger ☺


Roger Martineau, mv Ph.D.
Centre de recherche et de développement
sur le bovin laitier et le porc
Agriculture et agroalimentaire Canada/Agriculture and Agri-Food Canada
Téléphone/Telephone: 819-780-7319
Télécopieur/Facsimile: 819-564-5507
2000, Rue Collège / 2000, College Street
Sherbrooke (Québec)  J1M 0C8
Canada
roger.martineau at agr.gc.ca<mailto:roger.martineau at agr.gc.ca>


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