How effective PMI compared to log likelihood or chi square?

When comparing the effectiveness of Pointwise Mutual Information (PMI) with Log-Likelihood Ratio (LLR) or Chi-square (χ²) for bigram association measures, it's important to consider the characteristics and performance of each measure in relation to the specific task and dataset. Here are some factors to consider:

Sensitivity to Sparse Data: PMI tends to handle sparse data better than LLR and χ². Since sentiment analysis datasets often contain sparse data, PMI can provide more reliable and meaningful associations, even with low-frequency bigrams. LLR and χ² may struggle to produce robust associations when dealing with sparse data.
Balanced Handling of Positive and Negative Associations: PMI, LLR, and χ² can all capture both positive and negative associations. However, PMI is particularly effective in sentiment analysis because it can identify associations that indicate sentiment regardless of the polarity. It is crucial to detect both positive and negative sentiment indicators accurately, and PMI's ability to handle associations in both directions makes it suitable for this task.
Interpretability: PMI is often considered more interpretable than LLR and χ². PMI is based on the concept of information theory and provides a log-ratio that quantifies the strength of association. This log-ratio can be easily interpreted as a measure of how surprising or informative the association is. On the other hand, LLR and χ² values are statistical test statistics that indicate the deviation from independence, which may be less intuitive to interpret directly.
Computational Complexity: PMI, LLR, and χ² have similar computational complexity and are relatively efficient to compute. Therefore, the computational aspect is not a significant differentiator when comparing their effectiveness.

It's worth noting that the effectiveness of bigram association measures can vary depending on the specific dataset, task requirements, and the underlying characteristics of the text being analyzed. It's recommended to experiment with different measures and evaluate their performance on your specific sentiment analysis task to determine the most effective measure for your particular scenario.