Treatment effect over time

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  • #2627
    C.Dunn
    Participant

    Hello. I’m sure there must be a really straightforward statistical method I can use for the following problem, but I just seem to be going round in circles trying to find it. Even after reading Andy Field’s SPSS book!

    My experiment is very similar, I expect, to many other biologists: I have a number (5) of replicates of a plant, I have four treatment groups (including one control group which has had nothing added to it). The experiment starts with two weeks of stabilisation (nothing done to the plants). Once a week the carbon dioxide taken in by each plant (gas flux) is measured (this is conducted in such a way that each plant is measured at the same time).  The treatments are then added to the plants and once a week, for six weeks, the gas flux is measured. After the final measurement is taken the experiment ends.

    My aim is to see if the treatments have had an effect on the gas fluxes of the plants ie. has it increased/decreased compared to the control and which treatment has had the greatest effect.

    I’ve tried various ways of doing this, including grouping all the results together and conducting an independent ANOVA on them. However, I do not think this is taking into account the effect of time on the plants. Which is my main problem. Time is important (it causes the gas flux of all the plants to drop significantly, no matter what is done to them) but I want to specifically see the effect the treatments have on the plants.

    Anybody have any ideas? Apologies if this doesn’t make any sense at all!

    #2632
    Marco Bardus
    Member

    Hi C. Dunn,

    I would investigate the intervention effects by using a split-plot ANOVA (SPANOVA), in some books referred as mixed between-within subjects ANOVA (e.g., Tabachnick & Fidell’s, 2007, Pallant, 2010), which is also described in Andy Field’s book.

    (go to Analyze > General Linear Model > Repeated Measures) with “time” as your within-subject factor (independent within-subjects variable), the treatment conditions as independent between-subjects factors (categorial variable with 5 levels), and gas flux as your within-subjects dependent outcome variable (I guess it is continuous).

    I am aware of some criticisms about this technique, especially when the variables are not independent, but I think this is an easy way to investigate whether there are effects of time on your dependent variable. Perhaps those more stats savvy would have better recommendations.

    Kind regards,

    Marco

    Tabachnick, B. G., & Fidell, L. S. (2007). Using Multivariate Statistics (5th revised International ed.). Pearson Education.
    Pallant, J. (2010). SPSS Survival Manual: A Step by Step Guide to Data Analysis Using SPSS (4th ed.). Maidenhead, England: McGraw-Hill, Open University Press.
    #2631
    Anonymous
    Inactive

    the most common way i’ve seen biologist handle this kind of problems is through mixed-effects linear models (aka multilevel models, hierarchical linear models)… as Marco correctly pointed out, there have been quite a few issues have been pointed out concerning the ANOVA approach to handling time-varying, designs, which include (but are not restricted to):

     

    – the fact that they rely heavily on the almost unreasonable assumption of sphericity/compound symmetry (which are alternate ways of saying that the covariances among your variables stay the same over the whole course of the 5 replications)

     

    – the somewhat strange way in which most repeated-measures designs handle post-hoc comparisons (depending on who you read everyone different people advocate using different standard errors/mean-squared errors from the variance components that result from an analysis of variance)

     

    -the fact that the corrections in degrees of freedom for violating the assumptions of sphericity/compound symmetry dont always work in all cases…

     

    … and the list goes on.

     

    i guess depending on how used you are to working with linear models, you can choose mixed-design ANOVA/mixed-effcts regression, whichever one you find both easiest to understand and that best suits your data..

    #2630
    Marco Bardus
    Member

    ehehe, I heard about mixed models, and I wonder if the Mixed Models > Linear procedure is conducted in SPSS.

    How would you (Oscar) treat a situation like C.Dunn’s?

    I read that to treat repeated measures in linear mixed models you need to restructure the data and use the long format (if you have collected your DV in five different variables). I am not very familiar with this approach, though, but I see the potential and the (many) limitations of RMANOVA approach. It is very unlikely that the variances stay the same over time. I woul also add that RMANOVA does not account much for measurement error which is associated with each measurement occasion.

    An alternative approach could also include Latent Growth Curve modelling (or cross-lagged auto-regressive panel models) as implemented in structural equation modelling context.

    #2629
    Anonymous
    Inactive

    “long format”  just means… ok, imagine you have a matrix of data. if you use something like SPSS or excel  you would probably have a column for ” plant id” in order to identify which plant is receiving which treatment, and then 5 columns, each one for the 5 replicates. when you turn things into “long format” all you do is collapse those 5 columns into one with an indicator variable that will represent time, so, for example, if your sample size is 10 plants, you’d have 10 times the number “1” to indicate time 1 in your data-column “TIME” , then you’d copy-paste below those 10 plants the same data again and a “2” ten times on the data-column “TIME” and so on… it sounds confusing if you just read it, but if you look at an example with an actual matrix of data you’d be able to get right away what it means…

     

    i dont really use SPSS very often (i’m mostly an R user alongside with some Matlab and Mathematica) but i am aware it’s able to handle some traditional mixed-effects linear regression models…

     

    I think depending on what one feels more comfortable with, using Latent Growth Curves or Mixed-Effects linear models should give you the same answer. Muthen (2002) is probably the most famous among a long list of experts who have made the connections explicit between the parameterisation of both approaches so that most (if not all) mixed-effects regression models can be estimated via structural equation modeling and a lot of SEM can be done through mixed-effects linear models. you just have to think about the random effects like latent variables and shazam! there it is…

     

    if you were to ask *me* how i would do it, the traditional way would be like a mixed-effects regression with a random effect across measurement times and contrast-coding across different plant conditions, with the comparison condition being the one that did not receive any treatment… although nowadays i’m getting more and more into Markov processes so i would probably try and do it that way, even though i wouldn’t suggest this approach unless you know what you’re doing…heh…

    #2628
    darrin coe, ph.d.
    Participant

    I agreed the mixed anova with time as the repeated measure is the most straight foreword method and dr. field covers it fairly well.  you could always code time as a dummy variable and run it in a multiple regression — actually I thing the hierarchical regression would be better, because then you could see the effect of time alone and effect of time with treatments.  all independent variables can be recoded as dummy variables and you can set up the regression to consider interaction effects — all this interprets is scary.

    darrin coe, ph.d (I graduate on 2/26/12)

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