## Working Towards a Model

From the statistical point of view, length is the only response (dependent) variable. The first aim of this chapter is to develop a model that describes length as a function

Table 8.1 Illustration of the preparation of the spreadsheet. Eight columns were made that contained all the variables measured in the experiment. The first 48 rows are length measurements from series 1 (six replicates times eight treatments), and the next 48 rows from series 2. Notice that there should be 768 rows in total. However, due to missing values there are slightly less observations. We also created the nominal variable ID that indicates which observations are from the same batch. If there were no missing values, it would run from 1 to 128 (= 8 x 16), and each value would be repeated six times

Table 8.1 Illustration of the preparation of the spreadsheet. Eight columns were made that contained all the variables measured in the experiment. The first 48 rows are length measurements from series 1 (six replicates times eight treatments), and the next 48 rows from series 2. Notice that there should be 768 rows in total. However, due to missing values there are slightly less observations. We also created the nominal variable ID that indicates which observations are from the same batch. If there were no missing values, it would run from 1 to 128 (= 8 x 16), and each value would be repeated six times

 No Amino_FZ Propofol Ethanol Series Larvae Length ID 1 Without Without Without 1 L1 2.2 1 ó Without Without Without 1 L1 S.O 1 l With Without Without 1 L1 S.1 2 12 With Without Without 1 L1 S.S 2 1S Without With Without 1 L1 2.9 S 1S Without With Without 1 L1 2.9 S 19 Without Without With 1 L1 2.9 4 24 Without Without With 1 L1 S.O 4 2S With With Without 1 L1 2.S S SO With With Without 1 L1 S.S S S1 With Without With 1 L1 2.S ó S6 With Without With 1 L1 2.9 ó Sl Without With With 1 L1 S.O l 42 Without With With 1 L1 1.4 l 4S With With With 1 L1 1.9 S 4S With With With 1 L1 S.1 S 49 Without Without Without L2 S.ó 9 l1S With With With 1ó LSP 9.S 12S Table 8 .2 Available explanatory variables. The variables Amino_FZ, propofol, Ethanol and Larval stage are categorical. Series is a continuous explanatory variable that represents time Variable Nominal Remark

Amino_FZ Propofol Ethanol Series

Larval stage

Yes Yes Yes No Yes

Without and with

Without and with

Without and with

From 1 to 16 measured every 12 h

Amino_FZ Propofol Ethanol Series

Larval stage

Yes Yes Yes No Yes

Without and with

Without and with

Without and with

From 1 to 16 measured every 12 h

of the explanatory (independent) variables Amino_FZ, Propofol, and Ethanol, larval stage and time (called Series). Table 8.2 gives a description of all variables used in the study.

We now work towards a model of the form:

Length = function(Amino_FZ, Propofol, Ethanol, Series, Larval stage) (8.1)

This equation can be used to model the length as a function of the other variables.

The second question of interest is whether we can predict the age (time) of larvae removed from a body at the crime scene. This means that we get a sample from which we can measure the length, the larval stage, and drug combination, and we want to know the corresponding value of Series (post mortem interval). This is called inverse modelling (Draper and Smith 1998). Before addressing the inverse modelling problem, we need to find the best possible model in Eq. 8.1.

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