How do you balance model complexity and variance explained in statistical analysis?

When building statistical models, we are creating a simplified representation of a real-world phenomenon. This simplification process introduces two key sources of error: bias and variance. Bias: This represents the systematic error introduced by the model's assumptions. Variance: This reflects the model's sensitivity to the specific training data used. Thus the goal is to achieve a model with: Low Bias- The model accurately captures the underlying relationship between variables. Low variance- The model performs consistently well on both training and unseen data.

It is important to find the right balance between bias and variance. As you increase number of independent variables in the model, bias reduces however it leads to overfitting and poor performance in out of sample data, leading to higher variability. On the contrary if we simplify the model too much it can introduce bias in the model with large errors in training data set. Some methods to check right number of variables are AIC, adjusted R square

Efectivamente un modelo sin sesgo y con baja varianza representa mejor la distribución y le estabilidad a las proyecciones, pero encel mundo real podría asumir poco riesgo y por tanto menor retorno.

Utilize information criteria such as the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC) to compare models. These criteria balance model fit (variance explained) and complexity by incorporating a penalty term for the number of parameters.

It is important to not use too many variables in the model. Size of data also determine how many variables you could use. Such as model with very few data points <30,50 should have at max 2 variables. Can check impact of increasing variables using adjusted r square or AIC. Also model performance on out of sample should be tested and compared with metrics such as MAPE/RMSE in sample data. Cross validation can also be used in cases of less number of data points to be able to maximize on training on most of the available data.

Underfitting the data leads to bias in the model. It happens due to having very few independent variables. It leads to large errors in training data and highly likely chances of large errors in testing data. To improve the model performance, try to increase more variables, or use techniques like ARIMA model if needed

Below are some methods to check right amount of variables 1) adjusted r square 2) AIC 3) BIC 4) lasso regression ( penalizes more variables ) 5) ridge regression(specially helpful to treat multicollinearity, when independent variables are highly correlated)

Balancing model complexity and variance explained is a crucial aspect of statistical analysis. Increasing model complexity often leads to higher variance explained, but it can also result in overfitting, where the model performs well on the training data but poorly on new data. To strike the right balance, consider techniques like cross-validation, regularization, and model selection criteria (e.g., AIC, BIC) to find the simplest model that adequately explains the variance in the data without overfitting.

I feel I may have written the same thought on some other article regarding interpretability and complexity where, high bias-high variance models have better interpretability and lower efficacy compared to complex low bias - low variance models. As, high bias models possess loads of assumption limiting the model scope. Ideally, we need a balance between the two phenomena (bias and variance) as low variance models with low bias tend to have issues like overfitting. Lot of these can be resolved through adequate prepping pre-model fitting, thorough data understanding results in better model selection enhancing interpretability of outcomes and simplifying complexities.