22

The assumption that the relationships are the same at a finer level of aggregation is exactly the ecological fallacy. The problem, more generally, of the relationship depending on how you aggregate is the Modifiable Areal Unit Problem


10

+1 to Thomas' answer. That said, this is not always a bad idea. For instance, in forecasting, we frequently have a large number of noisy time series that we can reasonably expect to share some common dynamics. In such cases, it's common practice to estimate these common dynamics on an aggregate level and then impose them on the separate series we are ...


4

There are two quick and dirty solutions. First would be to disaggregate series B to weekly values (R package tempdisagg is great for that) and then do a usual model. Second aggregate series A to monthly frequency, do a forecast and then use disaggregation on the forecast. The more theoretical approach would be casting problem to a state space model. There ...


4

There are many traditional statistical approaches here, and none are a silver bullet for every circumstance. Sax and Steiner (2013; PDF link) collect several methods in the R package tempdisagg, namely Denton, Denton-Cholette, Chow-Lin, Fernandez and Litterman. [...] On the one hand, Denton (Denton, 1971) and Denton-Cholette (e.g. Dagum and Cholette, 2006)...


4

To verify the solution suggested in the great answer by @user20160 I prepared a toy example that demonstrates it. As suggested by @user20160, I am posting the code as a supplement to the answer. For explanations of this approach, check the other answer. First, let's generate the independent variable and append the column of ones to it, to use matrix ...


3

Here's an approach for solving this type of problem using latent variable models. It's not a specific model, but a general way to formulate a model by breaking the description of the system into two parts: the relationship between individual inputs and (unobserved) individual outputs, and the relationship between individual outputs and (observed) aggregate ...


2

Okay, I found out that what I was looking for is called a hierarchical linear models (see wikipedia). Just dropping that here, in case someone else encounters a similar problem.


2

I'm going to give an answer to a different question! Because I am unsure if the original one is tractable, but it is how I would frame the problem - so I hope it is helpful. Let's just start with the simpler task of decomposing a set of covariances between two spatial weights matrices for the same units of analysis. Lets say that $W = W^a + W^b$, and we ...


2

In addition to loss of statistical power, aggregation also adds potentially severe bias, particularly when there are non-linear associations between variables. As a rule, I vehemently oppose aggregation, unless there is a theoretical justification for doing so. The non-linear association issue comes up all over the place in actual data in my experience. ...


2

The question is addressed generally in the field referred to Aggregate Analysis. Here, for example, is an extract from a paper in this area: Aggregate analysis has been established as a standard method on the study of market response behavior for a long time. Aggregation has advanced our understanding of the linkages among social characteristics and ...


1

Generally, without additional assumptions, there is nothing we can say about the distribution of $x$ sampled at high frequency between the time points in which the actual observations have been sampled at low frequency. Imagine drawing the low-frequency points against time. There is an infinite amount of ways to connect the consecutive points, unless we ...


1

You are doing hierarchical forecasting, specifically using the top-down method. That is, you first forecast the aggregate, then break it down. An alternative would be the bottom-up method, where we first forecast daily orders, then aggregate them up. In top-down forecasting, there are of course different ways of disaggregating. What you are doing is ...


1

Different approaches could be appropriate depending on your goal. I'll describe one approach in case your goal is group-level prediction. You could use the individual-level features to build a bunch of aggregated features for each group (mean, std, median, max, min, ...). You now have richer features for each group which are likely to perform well on the ...


1

From the given information above, is it possible to assume $$\sigma_1 = \sqrt{0.2\sigma_F}, \sigma_2 = \sqrt{0.5\sigma_F}, \sigma_3 = \sqrt{0.3\sigma_F}$$ No, not at all. There's no reason the variance should partition in the same way the mean does. In a normal distribution, the two are totally separate from each other.


1

I have the same doubt as the initial question and did some checks on multi-level model or hierarchical linear models. Multi-level model does not seem to be a solution for this problem. As per my understanding, multi-level models are used when the independent variables are at different levels. In the given question, the dependent variable is the aggregated ...


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