17. Other models

Non-linear / Piecewise models

Piecewise Models

When the trend line seems to have different linear sections a piecewise model could be applied.

This could be done in Excel by graphing sections of the data

In iNZight copy the raw data file and delete sections in the file before uploading to iNZight again for analysis

Non-linear Models

Polynomial model

Multiplicative Models

but be careful about the limitations of its predictions.

How to do a multiplicative model (possible - but not needed for excellence)

Raw data graph (above) - notice the increase in height of the seasonal component so a multiplicative model would give better predictions.

We can analyse using Excel but this takes some time. (The iNZight method below is recommended)

Take the log(of the data) - notice the seasonal component (log) is now linearised.

In Excel we can derive the model: Prediction =10^(0.0018x + 4.2691+ASE)

From the graph of Log(y) vs (x) [excel spreadsheet], notice the predictions are more realistic

And how poor the Excel Additive model predictions are:

Multiplicative model using iNZight

Run iNZight as normal and load your data

'Manipulate Variables'

'Transform variables'

Drag your variable to be transformed into the 'Log (10)'

Notice how the variable has been transformed and added into your data table.

Plot the Log(data) graph

Notice that the end off the trend line drops due to the partial seasonal cycle (see the trend page for mare detail)

So we will remove some recent data to level the trend line (see the robustness page to find out how to remove data)

We then predict as normal - but remember we are predicting the 'Log(data)' values

Then we can convert them back to predictions by 10^iNZight value = Prediction

The table on the right compares iNZight's Additive Model Predictions compared with Multiplicative model predictions

Comparing the two methods:

Due to the emphasis on the recent effects in iNZight there is little difference between the predictions using the 'multiplicative' iNZight model and the normal 'Additive' model.

However using an Additive Excel Model in a situation where a multiplicative model would be better does lead to significantly inaccurate predictions. iNZight methods would be better.

All predictions using the 'Multiplicative' iNZight method lie well within the prediction interval for the normal iNZight additive model predictions.

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