Hi,
I have a continuous variable - which reflects a mean number based upon sample size - as a univariate time series. Values can be 0 or a positive float. We are conducting interrupted time series analysis on such using segmented regression. Data is neither seasonal nor autocorrelated.
I'm struggling to find the best model to fit to such data. I originally used Poisson, which fit the data well, but I'm aware shouldn't be used for non-integer data. Said models must also not allow for the model or confidence intervals to drop below 0. I don't think I can use a Gamma or Logistic Binomial as values can exceed 1.
Wondered if anyone had any thoughts on the most appropriate modelling point to start at?
perhaps, you may try to formulate your regression model as a non-linear optimization (most likely quadratic) subject to some certain constraints, where you can specify any constraints which you think must be imposed to (and satisfied by) the model - check for example here
https://www.ibm.com/support/pages/incorporate-constraints-regression-parameters
Since your continuous variable can take on non-negative values, a common approach to modeling such data is to use a linear regression model with a non-negative constraint on the predicted values. One way to do this is to use a generalized linear model (GLM) with a log link function and a gamma distribution for the response variable.
The gamma distribution is commonly used to model positive continuous data with right skewness, which appears to be the case for your data based on your description. The log link function is used to model the relationship between the mean response variable and the predictor variable in the log scale, which ensures that the predicted values are non-negative.
Another option to consider is the Tweedie distribution, which is a flexible distribution that can handle data with excess zeros, skewness, and heavy tails. The Tweedie distribution can be fitted using a GLM with a log link function, and it has a parameter that controls the degree of skewness and zero-inflation in the data.
In terms of confidence intervals, you can use a bootstrapping method to estimate confidence intervals for the regression coefficients and predicted values. Bootstrapping involves resampling your data with replacement and refitting the model to each resampled dataset to obtain a distribution of estimates. You can then use the percentile method to compute confidence intervals from the bootstrap distribution.
It's important to note that the choice of model depends on the specific characteristics of your data and the research question you are trying to answer, so it's always a good idea to consult with a statistician or data analyst to ensure that the modeling approach is appropriate for your needs.
Most important: what do you THEORETICALLY expect the model to be? What kind of data is it? Can you share some so we can have a look?
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