pair | twin | iq |
---|---|---|

112 | A | 113 |

112 | B | 109 |

114 | A | 94 |

114 | B | 100 |

126 | A | 99 |

126 | B | 86 |

# ASR003. Simple LMM - Twins’ IQ

The complete script for this example can be downloaded here:

### Dataset

In this example we will use the D002 dataset, and the first few rows are presented below:

### Model

The basic LMM that we will fit in this example is:

\[ y = \mu + twin + pair + e\ \] where,\(y\) is the IQ score,

\(\mu\) is the overall mean,

\(twin\) is the fixed effect of twin,

\(pair\) is the random effect of twin pair, with \(pair \sim \mathcal{N}(0,\,\sigma^{2}_{p})\),

\(e\) is the random residual effect, with \(e \sim \mathcal{N}(0,\,\sigma^{2}_{e})\).Now, let’s take a look at how to write the model with ASReml-R. Note that before fitting the model, `twin`

and `pair`

need to be set as factors.

```
<- asreml(
asr003 fixed = iq ~ twin,
random = ~pair,
residual = ~units,
data = d002
)
```

### Exploring output

Evaluate the significance of the fixed effects:

`wald(asr003, denDF = 'numeric')$Wald`

```
Df denDF F.inc Pr
(Intercept) 1 31 1499.000 0.00000000
twin 1 31 3.416 0.07412364
```

Having the factor `twin`

as not significant is relevant, as we are not expecting differences between them in terms of IQ.

Lets obtain the predicted means, based on the above model with:

`predict(asr003, classify = 'twin')$pvals`

```
twin predicted.value std.error status
1 A 93.21875 2.568317 Estimable
2 B 96.12500 2.568317 Estimable
```

We can also check the variance components:

`summary(asr003)$varcomp`

```
component std.error z.ratio bound %ch
pair 171.53572 48.84192 3.512059 P 0
units!R 39.56357 10.04961 3.936825 P 0
```

We can estimate the intra-correlation between twins (\(r^2\)), that, if close to one implies that we have a strong genetic component in this response variable. This can be done using:

`vpredict(asr003, r2 ~ V1/(V1+V2))`

```
Estimate SE
r2 0.8125831 0.06100241
```

Finally, we can report the random effects (BLUP) associated with each twin pair.

```
<- summary(asr003, coef = TRUE)$coef.random
BLUP head(BLUP)
```

```
solution std.error z.ratio
pair_112 14.639529 4.747755 3.0834633
pair_114 2.087359 4.747755 0.4396517
pair_126 -1.947267 4.747755 -0.4101449
pair_132 -14.499437 4.747755 -3.0539564
pair_136 -5.981893 4.747755 -1.2599414
pair_148 3.432234 4.747755 0.7229172
```

### More information

Note that an alternative of this model, using a more complex residual structure, can be found here: ASR025.