# What is lmer spitting out when verbose = TRUE?

Here’s a pretty terse and technical post, mostly so I don’t forget stuff.

Each iteration of the `lmer`

fitting algorithm is represented by a printed line, like this for example:

```
dl.lmer <- lmer(Ytrans ~ PC1 + (PC1 | snps), df, verbose = TRUE)
0: 2129.0419: 0.577350 0.617213 0.00000
1: 2067.3454: 1.54521 0.369388 -0.0426859
2: 2057.7418: 1.41456 0.597009 -0.0729722
3: 2050.2435: 1.21193 0.431843 -0.0347423
4: 2048.7592: 1.17166 0.504773 -0.0678838
5: 2048.6277: 1.09764 0.463493 -0.0386145
6: 2048.4524: 1.10305 0.471873 -0.0502234
7: 2048.3884: 1.11262 0.479344 -0.0595495
8: 2048.3731: 1.12189 0.478527 -0.0554404
9: 2048.3708: 1.12571 0.480838 -0.0579935
10: 2048.3705: 1.12540 0.480109 -0.0573556
11: 2048.3705: 1.12520 0.480096 -0.0574044
12: 2048.3705: 1.12479 0.480048 -0.0574280
13: 2048.3705: 1.12479 0.480042 -0.0574203
14: 2048.3705: 1.12479 0.480042 -0.0574203
```

The first column indexes the iteration. The second gives the value of the `-2 * summary(dl.lmer)@logLik`

. The remaining columns give the values of the variance component parameters. But what are these?

Well the short answer is that they are the elements of this slot in the resulting mer object,

```
dl.lmer@ST
[[1]]
(Intercept) PC1
(Intercept) 1.12478827 0.000000
PC1 -0.05742026 0.480042
```

Now this is a particularly simple model so `dl.lmer@ST`

is a list of length one. Still not confident on when longer lists will appear here. But what this means is that if this list element is multiplied by the transpose of itself, the result is proportional to the covariance matrix of the random effects,

```
dl.lmer@ST[[1]]%*%t(dl.lmer@ST[[1]])
(Intercept) PC1
(Intercept) 1.26514865 -0.06458564
PC1 -0.06458564 0.23373744
```

```
```

where the constant of proportionality is the residual variance. So that the variance matrix of the random effects is,

```
(summary(dl.lmer)@sigma^2) * dl.lmer@ST[[1]]%*%t(dl.lmer@ST[[1]])
(Intercept) PC1
(Intercept) 0.62467488 -0.03188955
PC1 -0.03188955 0.11540929
```

```
```