Understanding the mle estimation of dlm with DLmModReg and Error Code 11 from Lapack Routine dgesdd

Introduction to DLM

The Dynamic Linear Model (DLM) is a widely used statistical model for forecasting time series data. It is based on a linear Gaussian process, which allows it to capture complex patterns in the data while providing robust estimates of future values.

One of the primary functions of DLMs is to estimate the parameters of the underlying process that generates the observed time series data. This parameter estimation is typically done using Maximum Likelihood Estimation (MLE), which involves finding the optimal set of parameters that maximize the likelihood of observing the given data.

DLmModReg: A Function for Modeling and Estimating DLM Parameters

DLmModReg is a R function used to estimate the parameters of a DLM. It takes in several inputs, including:

• t: The time series data
• dV: The variance matrix of the process (a diagonal or square matrix)
• dW: The covariance matrix of the process (a diagonal or square matrix)
• bFun: A function that defines the linear predictor

When we call DLmModReg, it tries to fit a DLM model using the provided parameters and data. However, in this example, when we try to fit a DLM model like that:

library(dlm)
bFun = function(xi) { dlmModReg(t, dV=exp(xi[1]), dW=exp(xi[2:(2+ncol(t))]);  
fit = dlmMLE(Y, parm=rep(0, 1+ncol(t)), build=bFun);
}

we get the following error message:

Error in dlmLL(y = y, mod = mod, debug = debug) :  
error code 11 from Lapack routine dgesdd

Error Code 11 and Its Significance

The error code 11 is a generic error message that indicates an issue with the dgessd function. The dgessd function is a part of the LAPACK library, which is used for linear algebra operations.

In this case, the dgessd function is called when trying to calculate the eigenvalues and eigenvectors of the process covariance matrix. If there’s an issue with the input data or the computation itself, this function can return error codes like 11.

Why Is dgesdd Failing?

When we try to fit a DLM model using DLmModReg, it attempts to estimate the parameters by maximizing the likelihood of observing the given data. However, in our example, there are several issues that might be causing dgessd to fail:

• Non-singularity of dV and/or dW: If either dV or dW is not invertible (i.e., singular), then the process covariance matrix becomes non-regular. In this case, the dgessd function may return error code 11.
• Numerical instability or overflow: When working with large datasets or parameters, numerical instability can occur due to floating-point precision issues. This might cause dgessd to fail.
• Correlated data: If the input time series data is highly correlated (i.e., has strong autocorrelation), this can lead to singular or ill-conditioned matrices, which might trigger error code 11.

Resolving the Issue: Adjusting Parameters and Data Preprocessing

To resolve the issue of dgessd returning error code 11, we need to check our input data and parameter settings:

• Preprocess the data: Before fitting a DLM model, it is often useful to clean and preprocess your time series data. This might involve removing missing values, handling outliers, or applying transformations.
• Ensure proper initialization: Make sure that all parameters are properly initialized before calling DLmModReg. For instance, ensure that dV and dW have a valid and invertible structure.
• Check for numerical stability: Verify whether your data is causing any numerical instability issues. Try reducing the size of the dataset or using regularization techniques.

Code Adjustments

Here’s an adjusted version of our code with a focus on parameter adjustments:

library(dlm)
set.seed(123) # Set seed for reproducibility
t = matrix(rnorm(40*30), nrow=30, ncol=40) # Initialize time series data
dV = diag(20) # Initialize variance matrix with diagonal structure
dW = diag(10) # Initialize covariance matrix with diagonal structure

# Define linear predictor function
bFun = function(xi) { 
  exp(xi[1]) * t + exp(xi[2:(2+ncol(t))])
}

# Adjusted model parameters
fit = dlmMLE(Y, parm=rep(0, 1+ncol(t)), build=bFun)

Conclusion

In this article, we’ve explored the issue of dgessd returning error code 11 when fitting a DLM model using DLmModReg. We discussed potential causes and provided some solutions for adjusting parameters and data preprocessing.

To successfully fit a DLM model, it is essential to ensure that all input parameters are correctly initialized and that the data has been properly cleaned and transformed. Additionally, considering numerical stability issues can help prevent errors like dgessd returning error code 11.

Additional Considerations

When working with DLMs or other complex statistical models, there’s always more to learn. Here are some additional considerations:

• Regularization techniques: Regularization methods like L1 and L2 regularization can be used to stabilize the model.
• Numerical optimization methods: Using numerical optimization methods like gradient-based optimization or quasi-Newton methods can improve convergence speed.
• Model selection criteria: Choosing an appropriate model selection criterion, such as AIC or BIC, can help compare different models and choose the best one.

Last modified on 2024-05-19