why does chenard carries errors with a reproducible aligment file?

[Ingrid Schockaert]

Dear all,

I’m testing the chenard algoritm for small numbers, using the data for flanders from 308 municipalities, by age and sex (308*105*2). The test is to see up to what size of municipality, chenard works well enough to reproduce the number of emigrants by age and sex in the alignment file.

I first wanted to establish a baseline: the “perfectly reproducible alignment file” by age and sex. I did that by running an alignment file from observed migration data. Then I took the resulting migrations by age and sex produced by the chenard algoritm and reïntroduced that in the model as the perfectly reproducible aligment file. I figured that the “number of individuals missing” should be zero. But this was not the case. From the 278181 emigrants in the alignment file (total needed), 2452 were not aligned (missing individuals). I don’t understand why; I kept the same random seed (1000) and eliminated the random element from the algoritm (is_candidate: uniform () >0.0)

 

Here is the code:

Houshold level:

            select_int_emigrants:

                - migrant_pool: FALSE

                - num_persons: persons.count()

                - int_migration_targets: load('migration1.csv', type=int)##migration1.csv is an alignment file produced by the chenard algoritm.

                - is_candidate: uniform () >0.0 #replace by immigration_score

                - migrant_pool: align_abs(num_persons, int_migration_targets, filter=is_candidate, link=persons)

                - show("migrant pool", sum(migrant_pool * num_persons))

                - last_int_period: if(migrant_pool, period, 0) ### boolean/global

Individual level:

            migrant_pool:           

- int_migrated: FALSE

                - int_migrated: household.migrant_pool

       

            dump_info:

                - csv(groupby(res_id,age, gender, filter=int_migrated),

                      fname='migration2.csv')

Thanks in advance for any help!

Ingrid

[Gaëtan de Menten]

That is expected (even if counterintuitive) when you know what's inside Chenard's algorithm. The algorithm could be summarized like this: for each household,

* compute a relative need (the maximum of the household persons relative needs – i.e. how badly we need each person to fill the "bin" he belongs to),

* use that relative need as a probability of being selected

 

Now, in your first "pass" (when you create migration1.csv), you probably do not have the same targets than those in the second pass (where you use migration1.csv) because of the "error" (unaligned individuals) produced by the algorithm in the first pass, so the relative needs are different and thus the households being selected in the end are different even if the "raw" random numbers are the same.

 

Hope it helps,

Gaëtan

 

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[Ingrid Schockaert]

Dear Gaetan,

Thank you for your clear answer! Within the same exercice of getting to know Chenard-algoritm and its strenghts and weaknesses for small area migrations, I came across the next thing that puzzled me. Using the same code as before we simulated 3 years (2015-2017). The alignment files for each year are by age (0-94), sex and 308 municipalties. They are not the same for the 3 years. They are based on observations (the birth and death alignment are also based on observations, no hypotheses).

I then compared the needed numbers by age and sex with the number of individuals that emigrated in the simulation. The results are demonstrated in the graphs in attachment indicate for each year:
 -the alinged number of individuals by age (men), all municipalities confounded: black line
 -the simulated number of individuals by age (men), all municipalities confounded: green line

We observe:
 - a subestimated number of individuals between 15 and 30 and an overestimation of individuals between 40-60 and above 80.
 - these biases increase considerably over time!

It is the last observation that I don't understand and that is of important concern. Why does the discrepancy grow over time?
Do you have any idea why this is and what the solution might be?

Many thanks in advance,

Ingird

[Gaëtan de Menten]

Dear Ingrid,

 

I can only offer guesses. The subestimated and overestimated individuals might be due to how large (with more persons) households are selected first and I guess that in your dataset, larger households are more likely than average to contain individuals aged 40-60 and above 80, and less likely to contain individuals aged 15-50.

 

The growing problem might be due to either an aggravation of the above fact over time. If you plot total migrants but each period only compute new migrants, this could simply be due to a similar error in each period just accumulating over time.

Using align_abs(…, errors='carry') (which adjusts the targets automatically with the error of the last period) might help lower this problem (if you are in the second case).

[Ingrid Schockaert]

You wrote: I can only offer guesses. The subestimated and overestimated individuals might be due to how large (with more persons) households are selected first and I guess that in your dataset, larger households are more likely than average to contain individuals aged 40-60 and above 80, and less likely to contain individuals aged 15-50.

That is my guess also. Later I will adapt the "is_candidate - criterium" to order individuals by houshold size and houshold type, small and single housholds having some prefence. That is closer to reality and I presume that part of the age-distribution problem might also be solved. Is my assumption reasonable?

But the growing problem in time is still not clear to me. There is no reason why the above fact would be aggravated: if a child is born, it is added to the mother's houshold. If a person dies, the partner-id and mother-id is unset. It should not increase the household size of individuals age 40-60 or above 80. Does this sound correct?

I didn't understand the last part of your answer. It indead seems that the error is just cumulating, but if I understand correctly, I compute and plot only new migrants each year, since I put the variable 'is migrant' to false at each yearly run:

- entities:   
 - household:
   - select_int_emigrants:

                - migrant_pool: FALSE
                - num_persons: persons.count()

                - int_migration_targets: load('int_migration_targets.csv', type=int)

                - is_candidate: uniform () >0.0 #replace by immigration_score
                - migrant_pool: align_abs(num_persons, int_migration_targets, filter=is_candidate, link=persons)

- entities:   
 - person:
                 
            - migrant_pool:           

                - int_migrated: FALSE
                - int_migrated: household.migrant_pool

            - dump_info:
                - csv(groupby(res_id,age, gender, filter=int_migrated),
                      fname='simulation_{period}.csv',mode='a')     
                - csv(groupby(res_id, gender, filter=int_migrated),
                      fname='simulation_res_id_{period}.csv',mode='a')
                - csv(groupby(age, gender, filter=int_migrated),
                      fname='simulation_age_{period}.csv',mode='a')
                - csv(groupby(gender, filter=int_migrated),
                      fname='simulation_gender_{period}.csv',mode='a')

simulation:
    processes:
        - person: [ageing, birth, agegroup, death]
        - household: [select_int_emigrants]
        - person: [migrant_pool, dump_info]

regards,

Ingrid

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[Ingrid Schockaert]

Dear Gaetan,

Another problem arose when adding "errors='carry' " to the equation like this:

            select_int_emigrants: ###elk hh dat gaat migreren heeft een var "migrant_pool"

                - migrant_pool: FALSE
                - num_persons: persons.count()
                - int_migration_targets: load('int_migration_targets.csv', type=int)
                - is_candidate: uniform () >0.0 #replace by immigration_score

                - migrant_pool: align_abs(num_persons, int_migration_targets, filter=is_candidate, link=persons, errors='carry')

After one or two years of simulation, I get the following error message, when adding individuals from las period error:

adding 4597 individuals from last period error

ERROR: operands could not be broadcast together with shapes (308,95,2) (307,95,2) (308,95,2)

when evaluating: align_abs(household.num_persons, household.int_migration_targets, errors='carry', filter=household.is_candidate, link=One2Many(persons, hh_id, person))

Regards,

Ingrid

[Gaëtan de Menten]

Oops. This is a bug in the errors='carry' feature: it does not support the case where the "categories" are different from the previous period. I did not think about that case when I implemented the feature and it never occurred in our own models.

Sadly, it would be extremely difficult to fix in the current stable release (0.12) because that version does not include the foundations necessary to fix this (to be able to make the correspondence between two arrays by using labels instead of positions). This should be easier to fix with the next (0.13) release but that release is far from being ready.

I don't know what your "308" axis is (municipality?) but it seems like you have one less in one of the periods. Maybe you could investigate why that happens. It does not seem normal and it would probably help other parts of your code to fix this anyway.

Gaëtan

 

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