rail | travel |
---|---|

1 | 55 |

1 | 53 |

1 | 54 |

2 | 26 |

2 | 37 |

2 | 32 |

# ASR006. One-way classification LMM - Railways rails

The complete script for this example can be downloaded here:

### Dataset

In this example we will use the D004 dataset, and the first few rows are presented below:

### Model

The one-way classification LMM that we will fit is:

\[ y = \mu + rail + e\ \] where,\(y\) is the time for ultrasonic wave to travel the length of the rail,

\(\mu\) is the overall mean,

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

\(e\) 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 `rail`

needs to be set as factor.

```
<- asreml(
asr006 fixed = travel ~ 1,
random = ~rail,
residual = ~units,
data = d004
)
```

### Exploring output

The variance components estimated from this model are:

`summary(asr006)$varcomp`

```
component std.error z.ratio bound %ch
rail 615.73937 391.581893 1.572441 P 0.2
units!R 16.17798 6.606945 2.448633 P 0.0
```

Where the is a large component associated with `rail`

, indicating that this is a relevant source of variability.

The random effects (BLUPs) are:

```
<- summary(asr006, coef = TRUE)$coef.random
BLUP BLUP
```

```
solution std.error z.ratio
rail_1 -12.39122 10.33599 -1.198842
rail_2 -34.53019 10.33599 -3.340774
rail_3 18.00857 10.33599 1.742317
rail_4 29.24327 10.33599 2.829268
rail_5 -16.35641 10.33599 -1.582472
rail_6 16.02597 10.33599 1.550503
```