Test if observations are a constant proportion

Question

New to statistical testing, I may not be using the correct terminology in this question - I will try to explain as best I can.

I have secondary data where it is unclear if what appears to be a measured variable is actually a constant proportion of another variable. I have included a very small subset of that data below.

The variable in question is "Waste". I would like to test:

1. if the annual value for "Waste" is a constant proportion of "Dom.Supply" for each Country-Item pair, or if its variance is sufficient to decide the value for "Waste" has been measured separately from "Dom.Supply", and,
2. if "Waste" is a constant proportion of "Dom.Supply" for individual Country-Item pairs, if it is also constant between Country-Item pairs within a Region (Europe in this case).

It seems like an ANOVA may be appropriate? If so, would it be a test of whether first differences to the Country-Item mean are equal to zero? The number of Country-Item pairs is about 3100 (143 x 22); countries are aggregated into 7 global regions.

Does the time-series nature of this dataset complicate things?

Thanks

Country Group   Item    Year    Dom.Supply  Waste
Bulgaria    Cereals Wheat   1961    2385    274
Bulgaria    Cereals Wheat   1962    2307    262
Bulgaria    Cereals Wheat   1963    2411    277
Bulgaria    Cereals Wheat   1964    2521    286
Bulgaria    Cereals Wheat   1965    2661    341
Bulgaria    Cereals Wheat   1966    2756    385
Bulgaria    Cereals Wheat   1967    2668    357
Bulgaria    Cereals Wheat   1968    2752    349
Bulgaria    Cereals Wheat   1969    2836    343
Bulgaria    Cereals Wheat   1970    2870    344
Bulgaria    Cereals Barley  1961    676 15
Bulgaria    Cereals Barley  1962    640 16
Bulgaria    Cereals Barley  1963    713 16
Bulgaria    Cereals Barley  1964    927 21
Bulgaria    Cereals Barley  1965    1008    22
Bulgaria    Cereals Barley  1966    1063    24
Bulgaria    Cereals Barley  1967    983 23
Bulgaria    Cereals Barley  1968    846 19
Bulgaria    Cereals Barley  1969    933 20
Bulgaria    Cereals Barley  1970    1278    27
Czechoslovakia  Cereals Wheat   1961    2768    100
Czechoslovakia  Cereals Wheat   1962    2816    100
Czechoslovakia  Cereals Wheat   1963    2864    100
Czechoslovakia  Cereals Wheat   1964    3042    110
Czechoslovakia  Cereals Wheat   1965    3548    110
Czechoslovakia  Cereals Wheat   1966    3620    150
Czechoslovakia  Cereals Wheat   1967    3924    180
Czechoslovakia  Cereals Wheat   1968    4495    180
Czechoslovakia  Cereals Wheat   1969    4238    200
Czechoslovakia  Cereals Wheat   1970    4657    250
Czechoslovakia  Cereals Barley  1961    1412    98
Czechoslovakia  Cereals Barley  1962    1602    105
Czechoslovakia  Cereals Barley  1963    1532    100
Czechoslovakia  Cereals Barley  1964    1745    108
Czechoslovakia  Cereals Barley  1965    1373    110
Czechoslovakia  Cereals Barley  1966    1496    108
Czechoslovakia  Cereals Barley  1967    1743    120
Czechoslovakia  Cereals Barley  1968    2049    120
Czechoslovakia  Cereals Barley  1969    2408    123
Czechoslovakia  Cereals Barley  1970    2221    120

Answer 1

I'm not very good at time series analysis, but I don't see any obvious advantages with time series analysis over a mixed model regression analysis method.

It seems to me you have some sort of count data as your dependent variable, and I would try to model it using a Poisson or negative binomial distributional assumption. I would like to use Year and Dom.Supply as a quadratic or perhaps cubic function to model non-linearity, and country and Item as random effects (possibly also global region as a random effect, or as a fixed effect). Interaction terms might also be considered. A basic model might look something like this:

Waste ~ Year + I(Year^2) + Dom.Supply + I(Dom.Supply^2) + (1|Item) + (1|Country)

The package glmmADMB for R allows for these kinds of models with a negative binomial distributional assumption.