6 Modelling Scientific Systems – in development
You have already identified (step 1) your aims in relation to modelling the system that you are investigating.
ACTION: You now need to
identify the actual measurements that you must make to achieve each of your aims.
The measurements are grouped under the headings of modelling -
Linear variation
Exponential variation
Non-linear variation
Variation with respect to more than one other variable
Any more?
Linear variation of a response variable, y, with respect to a single predictor variable, x - 'best-fit' straight line.
> Linear regression of y against x to derive slope and intercept of 'best-fit' straight line. Excel Minitab, SPSS
Note: Normal linear regression assumes that there is no uncertainty in the x values.
> Use Orthogonal regression when there is uncertainty in the values of both y and x.
> Use Logical regression when response variable, y, has binary values (e.g. Yes/No)
> Using 'best-fit' straight line (calibration line) to predict (read off) unknown values
Exponential variation of a response variable, y, with respect to a single predictor variable, x.
> Log transformation to ln(y) followed by linear regression against x
> Using non-linear regression in software.
Non-linear variation of a response variable, y, with respect to a single variable, x.
> Transformation of data followed by linear regression
> Using non-linear regression in software
> Using Excel Solver
Variation of a response variable with respect to two or more variables
> Stepwise regression
> ANOVA
Does the value of one variable change in ordered way with a change in the value of another variable?
Examples:
Does a measurement of body fat using skinfold thickness give the same results as using bioelectrical impedance?
Typical analyses: Pearson’s correlation (N), Linear Regression (N), Bland-Altman plot, Spearman’s correlation
Can I produce a mathematical model to show how certain factors affect the measured response variable(s)?
Examples:
Producing an equation to predict lung function, based on physiological factors (e.g age, blood pressure, exercise, body fat, etc)?
Typical analyses: Stepwise linear (or multiple) regression,
What is the variation of a measured variable with respect to time?
Examples:
How do cannabis samples degrade with heat and time?
Calculations based on exponential decay (or growth)
Typical analyses: Plot of log(data) against time, linear regression (N)
Does the measured variable change linearly with respect to a factor variable?
Examples:
Using a linear calibration curve
Typical analyses: Linear regression (N)