Application of information theory-based decision support system for high precision modeling of the length-weight relationship (LWR) for five marine shrimps from the northwestern Bay of Bengal

The study was conducted to develop an information theory-based decision support system to understand the variance distribution structure of the data so that a proper modeling approach could be implemented to explain the relationship between the body length and weight of shrimps. Based on biological reasoning, initially, a log-normal multiplicative error structure was assumed and therefore, a log-linearized model was applied. Secondly, the support for normal additive error structure was assessed by fitting a weighted nonlinear model with a power variance structure (wNLM) to address the heteroscedasticity in shrimp weight. The likelihood support for the error structures was ascertained by comparing the AICc of the two competing models. As the general cut-off criterion (Δ AICc>2.0) did not give conclusive evidence from the scrutiny of the probability density diagnostic plot of the residuals, an alternative model scaling criteria, i.e., Akaike weight (Aw) of 0.9 was used for model selection. The corresponding Δ AICc cut-off score of 4.2 was estimated by regressing the Δ AICc score of the competing model against the Aw scores of the best model. The competing models with Δ AICc > 4.2 were rejected and the alternate models with Aw ≥ 0.9 were selected for modeling the length–weight relationship. Both the models were observed to be well founded, as narrow differences in the root mean squared error (RMSE) were observed. A lower RMSE was almost always observed from wNLM despite a higher Δ AICc score, which indicates that RMSE may not be efficient in detecting the model overfitting issue. Contrary to popular belief, only 26.7% of the datasets exhibited a log-normal error structure, whereas, a normal error structure was evident in 33.3% of the datasets. Interestingly, 40.0% of the datasets showed data ambivalence (Δ AICc < 4.2) and therefore, an Akaike weighted model averaging was performed to reduce model uncertainty for the accurate estimation of model parameters and their confidence intervals.