Dear All, I am analysing some data for a colleague (not my data, gotta be published so I cannot divulge). My response variable is the number of matings observed per day for some fruitlies. My factors are: Day: the observations were taken on 9 days Regime: 3 selection regimes Line: 3 replicates per selection regime. I have 81 observations in total The lines are coded A to I, so I do not need to do any extra grouping. my model is: anova(lme(Matings ~ Day * Regime, random = ~1| Line/Day, mydata)) I would expect to have: 1 df per Day 2 df per Regime 2 df per Day * Regime 6 df per Line %in% Regime 6 df per Day * Line %in% Regime, so my anova would have: numDF denDF int 1 63 Day 1 6 Regime 2 6 D*R 2 6 what I get is: numDF denDF int 1 69 Day 1 69 Regime 2 6 D*R 2 69 why is lme not calculating correctly the Line/Day interation ? I am using R 1.7.0 under W2K, although I updated the packages and I get the warning "nlme lib built under R1.7.1..." Regards, Federico ========================= Federico C.F. Calboli Department of Biology University College London Room 327 Darwin Building Gower Street London WClE 6BT Tel: (+44) 020 7679 4395 Fax (+44) 020 7679 7096 f.calboli at ucl.ac.uk
degrees of freedom in a LME model
3 messages · Federico Calboli, Douglas Bates
4 days later
Federico Calboli <f.calboli at ucl.ac.uk> writes:
Dear All, I am analysing some data for a colleague (not my data, gotta be published so I cannot divulge). My response variable is the number of matings observed per day for some fruitlies. My factors are: Day: the observations were taken on 9 days Regime: 3 selection regimes Line: 3 replicates per selection regime. I have 81 observations in total The lines are coded A to I, so I do not need to do any extra grouping. my model is: anova(lme(Matings ~ Day * Regime, random = ~1| Line/Day, mydata)) I would expect to have: 1 df per Day 2 df per Regime 2 df per Day * Regime 6 df per Line %in% Regime 6 df per Day * Line %in% Regime, so my anova would have: numDF denDF int 1 63 Day 1 6 Regime 2 6 D*R 2 6 what I get is: numDF denDF int 1 69 Day 1 69 Regime 2 6 D*R 2 69 why is lme not calculating correctly the Line/Day interation ?
I think your calculation is based on using only within-strata information whereas lme uses both within-strata and between-strata information for estimates of effects. The way that we calculate denominator degrees of freedom is described on pp. 90-91 of Pinheiro and Bates (2000). For each term in the fixed-effects we determine the innermost level of the random effects at which is it changing. Because Regime is constant for each Line it has the fewest degrees of freedom but Day is changing within Line so terms in Day have more degrees of freedom. Is this what you intended? I must admit I am having difficulty understanding the structure of the experiment but it is still Monday morning for me so perhaps that is not surprising.
I am using R 1.7.0 under W2K, although I updated the packages and I get the warning "nlme lib built under R1.7.1..." Regards, Federico
Douglas Bates bates at stat.wisc.edu Statistics Department 608/262-2598 University of Wisconsin - Madison http://www.stat.wisc.edu/~bates/
Dear Prof. Bates, Thank you for your reply. I did actually check the book at pages 89-92, but I have to say I found it a bit "cryptic", if not downright confusing, for a genetist like me. Any day of the week. To use the example in the book, I cannot see why MACHINE is inner to WORKER. Or where the Pi = sum of df for the term estimatet at level i... To me it's just a two way anova with one random effect + one interaction. My df correspond to those in the book, but I calculated them in the "bog standard" way of 2 df for 3 machines, 5 df for 6 workers and 2 * 5 = 10 df for the interaction...oh well... I attach the datasest (I did a sample with replace = TRUE, should have thought of this earlier...). I hope thing would be clearer. It is obvious that if I consider day a "factor", as I have just one datapoint per day per line within regime, I end up using all my degrees of freedom: 2 df for 3 regimes 6 df for line within regime 8 df for day (9 days, day as factor) 16 df for regime * day 48 df for line * day total 80 df, with 0 df remaining for the error. A bit of a problem I daresay, but I did not collect the data! BUT I did calculate my anova considering day as a continuous variable, 2 df for 3 regimes 6 df for line within regime 1 df for day (day as a number) 2 df for regime * day 6 df for line * day total 17 df, with 63 df remaining for the error. I still do not get why the interaction term Regime*Day is not tested on the interaction Line-in-regime*Day... In my analysis LME is clumping Error and Line-in-regime*Day together, judging by the df I was talking about in my previuos email. To me it should be just another "bog standard" situation...But if I were smart enough to be a statistician I would not be here doing genetics ;) Regards, Federico Calboli Day Line Regime Matings 2 501 es 0.4 4 501 es 0.32989691 9 501 es 0.48484848 11 501 es 0.72727273 16 501 es 0.34042553 18 501 es 0.56470588 25 501 es 0.37509377 30 501 es 0.22222222 32 501 es 0.77777778 2 502 es 0.57142857 4 502 es 1.06666667 9 502 es 0.16 11 502 es 0.4 16 502 es 0.4 18 502 es 0.33333333 25 502 es 0.80808081 30 502 es 0.48 32 502 es 0.25531915 2 503 es 0 4 503 es 0.72727273 9 503 es 0.3 11 503 es 0.77777778 16 503 es 0.34042553 18 503 es 1.06666667 25 503 es 0.32989691 30 503 es 1.24444444 32 503 es 0.19153725 2 fb1 fb 0.72727273 4 fb1 fb 0.42105263 9 fb1 fb 0.32989691 11 fb1 fb 0.32323232 16 fb1 fb 0.37509377 18 fb1 fb 0.51612903 25 fb1 fb 0.4 30 fb1 fb 0.24742268 32 fb1 fb 0.24742268 2 fb2 fb 1.33333333 4 fb2 fb 0.25263158 9 fb2 fb 0.66666667 11 fb2 fb 1.06666667 16 fb2 fb 0.97959184 18 fb2 fb 0.42105263 25 fb2 fb 0.57142857 30 fb2 fb 1.15555556 32 fb2 fb 0.80808081 2 fb3 fb 0.18952106 4 fb3 fb 0.66666667 9 fb3 fb 1.22033898 11 fb3 fb 0.35955056 16 fb3 fb 1.68421053 18 fb3 fb 0.57461174 25 fb3 fb 0.93506493 30 fb3 fb 0.80808081 32 fb3 fb 0.57461174 2 mb1 mb 0.22222222 4 mb1 mb 0.3902439 9 mb1 mb 0.42105263 11 mb1 mb 0.48484848 16 mb1 mb 0.55555556 18 mb1 mb 1.68421053 25 mb1 mb 0.4 30 mb1 mb 0.16 32 mb1 mb 0.09523809 2 mb2 mb 0.77777778 4 mb2 mb 0.68817204 9 mb2 mb 0.25263158 11 mb2 mb 1.33333333 16 mb2 mb 0.5 18 mb2 mb 0.37509377 25 mb2 mb 0.16494845 30 mb2 mb 2.46153846 32 mb2 mb 0.47058824 2 mb3 mb 1.06666667 4 mb3 mb 0.5 9 mb3 mb 0.5 11 mb3 mb 0.38095238 16 mb3 mb 0.26373626 18 mb3 mb 0.87912088 25 mb3 mb 0.55555556 30 mb3 mb 0.74418605 32 mb3 mb 1.33333333
I think your calculation is based on using only within-strata information whereas lme uses both within-strata and between-strata information for estimates of effects. The way that we calculate denominator degrees of freedom is described on pp. 90-91 of Pinheiro and Bates (2000). For each term in the fixed-effects we determine the innermost level of the random effects at which is it changing. Because Regime is constant for each Line it has the fewest degrees of freedom but Day is changing within Line so terms in Day have more degrees of freedom. Is this what you intended? I must admit I am having difficulty understanding the structure of the experiment but it is still Monday morning for me so perhaps that is not surprising.
========================= Federico C.F. Calboli Department of Biology University College London Room 327 Darwin Building Gower Street London WClE 6BT Tel: (+44) 020 7679 4395 Fax (+44) 020 7679 7096 f.calboli at ucl.ac.uk