‘Model’ refers to…

My blog is titled Freya’s Research, but to date, there has (rather sneakily) been a lack of posts related to what I actually do here in the QAEco lab.   Unfortunately, I don’t just look at orchids and take photos of Acacia.

Caladenia alpina (orchid), Acacia sp. (wattle) and Diuris sp. (orchid)

A large part of my PhD will be building a hierarchical Bayesian model that incorporates plant functional traits as species level predictors of plant growth and reproduction.

In my next couple of posts I will endeavor to explain all these terms (but don’t worry there will also be a few posts about what is flowering around Melbourne). For my first post in this series about my research, I would like to start from the start and try to explain what a model is.

Needless to say, googling “model” gives you mixed results. I found it easier to ask my Supervisor for a good book on modelling.  The result of this was a book, ‘How to Model It, Problem solving for the Computer Age’ by Anthony Starfield, Karl Smith and Andrew Bleloch.

These authors suggest that models are formalisations of the relationships between things.

There are many types of models:

•  mental models
• graphical models
• statistical models
• mathematical models

A mathematical or statistical model, concerns the relationships between quantifiable things or values. Values that are actively changing are called variables, values that are less likely to change are parameters (these can mediate the effect of variables). Parameters that can’t be changed are called constants.

Hardenbergia violacea (is flowering outside at the moment)

How to model it begins with the authors posing a problem; “how long will it take you to read this book?” A length of time immediately pops into ones head. But, if you go to the trouble of really thinking about it (which the book makes you do), you might find that the time it will take may depend on a few things.

Maybe the time it takes to read the book will depend on how fast I read one page, and then on how many pages there are in the book. Maybe it will depend on the number of tasks I have to do on each page and the time it takes me to do each task (maybe how many things are in flower outside?).

If I take my mental model a bit further, I can formulate a simple equation:

T = pP + wWP

Where:

T = time taken to read the book,
p = time to read one page of the book,
P = number of pages in the book,
W = number of ‘tasks’ per page, and
w = time taken to complete each task

P,  W, and  w changes between different books and so these are variables (because they are actively changing).  p may not change as much from book to book, as everyone probably has an their own average reading time. Therefore, p is a parameter.

The authors of How to model it show that we all make (mental) models all the time.

A model is a purposeful representation of something. Models can be used for synthesising information, for estimating values of important variables, for prediction, decision-making and explanation.  One major benefit of using a formal model is that you’re forced to be explicit about your thought processes. It can be quite challenging and very revealing when you’re confronted with all your assumptions.

In my research I will be a using a type of statistical model called a hierarchical  Bayesian model.  My aim is to model plant growth and reproduction incorporating the influence of species-specific plant functional traits.

Of course, an important consideration should always be what the point of your model is.  Indeed the authors of How to model it suggest you should always ask yourself three questions:

• What (exactly) am I doing? (I should be able to describe it precisely)
• Why am I doing it? (How does it fit into the solution)
• How will it help? (What will I do with the outcome once I have it)

Acacia pycnantha inflorescence

Great questions to ask oneself.  What’s the point?   Why do I want to model plant growth and reproduction?  Why don’t I just spend all my time taking photos of orchids and Acacias?   The answers to all this and more will pop up in a future post or two.

In my next blog, however, I will attempt to give an overview of the ‘hierarchical’ bit of my modelling approach.

Stay tuned…

Ref:

Starfield AM, Smith KA & Bleloch AL (1994) How to model it, problem solving for the computer age.  McGraw Hill, New York.

Thanks to W.K Morris for proof reading.