trt | patient | weight | loss |
---|---|---|---|

trtA | 1 | 198 | 2 |

trtA | 2 | 207 | 3 |

trtA | 3 | 262 | 8 |

trtA | 4 | 189 | 1 |

trtA | 5 | 230 | 3 |

trtA | 6 | 278 | 5 |

trtA | 7 | 222 | 3 |

trtA | 8 | 240 | 4 |

# ASR019. Obtaining predictions for specific values of an explanatory variable - Synthetic weight loss data

The complete script for this example can be downloaded here:

### Dataset

The model that we will fit here is based on the D015 synthetic dataset, and the first few rows are presented below:

### Model

In this example we will fit a linear model with the following specification:

\[ y = \mu + trt + weight + trt:weight + e\ \]

where,\(y\) is the yield of oats,

\(\mu\) is the overall mean,

\(trt\) is the fixed effect of treatment,

\(weight\) is the fixed effect of the initial weight,

\(trt:weight\) is the fixed effect of the interaction between treatment and initial weight,

\(e\) 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, `trt`

needs to be set as factor.

```
<- asreml(
asr019 fixed = loss ~ trt + weight + trt:weight,
residual = ~units,
data = d015
)
```

The above model has only fixed effects, and a simple residual term.

### Exploring output

Let’s take a look at the ANOVA table:

`wald(asr019, denDF = 'numeric', ssType = 'conditional')$Wald`

```
Df denDF F.inc F.con Margin Pr
(Intercept) 1 18 292.800 27.600 5.381724e-05
trt 2 18 61.920 61.160 A 9.410860e-09
weight 1 18 60.280 60.280 A 3.743320e-07
trt:weight 2 18 6.178 6.178 B 9.061740e-03
```

Note that in this case, we are using `ssType = 'conditional'`

, which allows for testing the significance of each model term given that *all other* terms are included in the model. This is in contrast to the `sequential`

options that is used by default that tests the terms in a sequential order.

We can calculate the predictions such as:

`predict(asr019, classify = 'trt:weight')$pvals`

```
trt weight predicted.value std.error status
1 placebo 235.5833 1.914169 0.5374119 Estimable
2 trtA 235.5833 4.050402 0.5481806 Estimable
3 trtB 235.5833 9.751260 0.5324321 Estimable
```

Here we can see the predictions of the different treatments based on the average initial weight of 235.6 pounds.

However, if we are interested to estimate predictions based on specific initial weight values, it is possible to add another component to the function `predict()`

as shown in the following code:

`predict(asr019, classify = 'trt:weight', levels = list(weight = c(190, 230, 270)))$pvals`

```
trt weight predicted.value std.error status
1 placebo 190 0.05409661 0.9505139 Estimable
2 placebo 230 1.68633574 0.5569940 Estimable
3 placebo 270 3.31857486 0.6990672 Estimable
4 trtA 190 1.40614042 0.8806557 Estimable
5 trtA 230 3.72651645 0.5323593 Estimable
6 trtA 270 6.04689249 0.9327052 Estimable
7 trtB 190 4.51815708 0.9063103 Estimable
8 trtB 230 9.11027680 0.5445855 Estimable
9 trtB 270 13.70239653 0.7268101 Estimable
```

Now, we are able to obtain predictions on how effective the different treatments are based on a given initial weight of a patient.