## Logit Regression Results ### Overview The image contains a series of Logit Regression Results, each presenting statistical analysis for different models and conditions. Each result includes details such as the dependent variable, number of observations, model type, date, log-likelihood, convergence status, covariance type, and coefficients with standard errors, z-values, and p-values. The results also describe the effect of subjects or conditions with specific attributes. ### Components/Axes Each Logit Regression Result section contains the following components: * **Dep. Variable:** Dependent variable name (e.g., "respondent scores") * **Model:** Model type (e.g., "MLE DI Model") * **Date:** Date of analysis (e.g., "Tue, 04 Jun 2024") * **Log Likelihood:** Log-likelihood value * **Converged:** Indicates whether the model converged * **Covariance Type:** Type of covariance used (e.g., "nonrobust") * **Pseudo R-squared:** Pseudo R-squared value * **LLR p-value:** Likelihood Ratio Test p-value * **No. Observations:** Number of observations * **Intercept:** Intercept coefficient, standard error, z-value, and p-value, and confidence interval * **Coefficient(s):** Coefficient name, standard error, z-value, and p-value, and confidence interval * **Effect of subject/condition:** Description of the effect being analyzed * **Current function value:** Current function value * **Function evaluations:** Number of function evaluations * **Gradient evaluations:** Number of gradient evaluations ### Detailed Analysis or ### Content Details Here's a breakdown of the extracted data from each Logit Regression Result section: **Result 1:** * Dep. Variable: respondent scores * No. Observations: 96 * Model: MLE DI Model * Date: Tue, 04 Jun 2024 * Log Likelihood: -62.83 * Pseudo R-squared: 0.05200 * Converged: True * Covariance Type: nonrobust * LLR p-value: 0.05200 * Intercept: * coef: -0.2121 * stderr: 0.668 * z: -0.318 * P>|z|: 0.751 * [0.025 0.975]: -1.522, 1.098 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tnumeric::multi_attribute]]: * coef: 0.2101 * stderr: 0.626 * z: 0.336 * P>|z|: 0.737 * [0.025 0.975]: -1.018, 1.438 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tcategorical::multi_attribute]]: * coef: 0.6696 * stderr: 0.532 * z: 1.259 * P>|z|: 0.208 * [0.025 0.975]: -0.373, 1.712 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tnumeric::multi_attribute, Tcategorical::multi_attribute]]: * coef: 0.420 * stderr: 0.420 * z: 1.001 * P>|z|: 0.317 * [0.025 0.975]: -0.403, 1.243 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Talgorithmic::multi_attribute]]: * coef: 1.477 * stderr: 0.740 * z: 2.00 * P>|z|: 0.046 * [0.025 0.975]: 0.027, 2.927 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tnumeric::multi_attribute, Talgorithmic::multi_attribute]]: * coef: 0.140 * stderr: 0.577 * z: 0.243 * P>|z|: 0.808 * [0.025 0.975]: -0.991, 1.271 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tcategorical::multi_attribute, Talgorithmic::multi_attribute]]: * coef: -0.203 * stderr: 0.526 * z: -0.386 * P>|z|: 0.700 * [0.025 0.975]: -1.234, 0.828 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tnumeric::multi_attribute, Tcategorical::multi_attribute, Talgorithmic::multi_attribute]]: * coef: 1.444 * stderr: 0.844 * z: 1.712 * P>|z|: 0.087 * [0.025 0.975]: -0.210, 3.098 * C[subject_type, Treatment/reference=d[Talgorithmic::multi_attribute]]: * coef: 0.2148 * stderr: 0.379 * z: 0.567 * P>|z|: 0.571 * [0.025 0.975]: -0.529, 0.968 * C[subject_type, Treatment/reference=d[Tcategorical::multi_attribute]]: * coef: 0.529 * stderr: 0.567 * z: 0.933 * P>|z|: 0.351 * [0.025 0.975]: -0.582, 1.640 * C[subject_type, Treatment/reference=d[Tnumeric::multi_attribute]]: * coef: -0.612 * stderr: 0.8001 * z: -0.765 * P>|z|: 0.444 * [0.025 0.975]: -2.180, 0.956 * C[subject_type, Treatment/reference=d[Tnumeric::multi_attribute, Tcategorical::multi_attribute]]: * coef: -0.251 * stderr: 0.586 * z: -0.428 * P>|z|: 0.669 * [0.025 0.975]: -1.400, 0.898 * C[subject_type, Treatment/reference=d[Tnumeric::multi_attribute, Talgorithmic::multi_attribute]]: * coef: 1.378 * stderr: 1.168 * z: 1.179 * P>|z|: 0.238 * [0.025 0.975]: -0.912, 3.667 * C[subject_type, Treatment/reference=d[Tcategorical::multi_attribute, Talgorithmic::multi_attribute]]: * coef: 0.947 * stderr: 1.378 * z: 0.687 * P>|z|: 0.492 * [0.025 0.975]: -1.754, 3.648 * Degrees of freedom: 4 * Likelihood ratio is 11.6001 * p value for the significance of model improvement when including interaction terms is 0.020686001787547076 * Effect of subject with only the conditions [categorical] * Current function value: 0.654493 * Optimization terminated successfully * Function evaluations: 12 * Gradient evaluations: 12 **Result 2:** * Dep. Variable: respondent scores * No. Observations: 96 * Model: Logit DI Model * Date: Tue, 04 Jun 2024 * Log Likelihood: -64.104 * Pseudo R-squared: 0.02782 * Converged: True * Covariance Type: nonrobust * LLR p-value: 0.05007 * Intercept: * coef: -1.457 * stderr: 0.733 * z: -1.988 * P>|z|: 0.047 * [0.025 0.975]: -2.905, -0.009 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tnumeric::multi_attribute]]: * coef: -0.8109 * stderr: 0.430 * z: -1.879 * P>|z|: 0.060 * [0.025 0.975]: -1.657, 0.035 * Effect of subject with only the conditions [multi_attribute] * Current function value: 0.661403 * Optimization terminated successfully * Function evaluations: 9 * Gradient evaluations: 10 **Result 3:** * Dep. Variable: respondent scores * No. Observations: 96 * Model: Logit DI Model * Date: Tue, 04 Jun 2024 * Log Likelihood: -66.521 * Pseudo R-squared: 0.01664 * Converged: True * Covariance Type: nonrobust * LLR p-value: 0.1368 * Intercept: * coef: -0.2889 * stderr: 0.420 * z: -0.688 * P>|z|: 0.491 * [0.025 0.975]: -1.112, 0.534 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tnumeric::multi_attribute]]: * coef: 0.2152 * stderr: 0.269 * z: 0.800 * P>|z|: 0.423 * [0.025 0.975]: -0.312, 0.742 * Effect of subject with only the conditions [numeric] * Current function value: 0.688033 * Optimization terminated successfully * Function evaluations: 10 * Gradient evaluations: 11 **Result 4:** * Dep. Variable: respondent scores * No. Observations: 104 * Model: Logit DI Model * Date: Tue, 04 Jun 2024 * Log Likelihood: -70.855 * Pseudo R-squared: 0.001360 * Converged: True * Covariance Type: nonrobust * LLR p-value: 0.6607 * Intercept: * coef: -1.491 * stderr: 0.159 * z: -9.375 * P>|z|: 0.000 * [0.025 0.975]: -1.803, -1.179 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tnumeric::multi_attribute]]: * coef: -0.1748 * stderr: 0.457 * z: -0.382 * P>|z|: 0.702 * [0.025 0.975]: -0.977, 0.619 * Effect of subject with only the conditions [numeric, multi_attribute] * Current function value: 0.688076 * Optimization terminated successfully * Function evaluations: 9 * Gradient evaluations: 10 **Result 5:** * Dep. Variable: respondent scores * No. Observations: 96 * Model: Logit DI Model * Date: Tue, 04 Jun 2024 * Log Likelihood: -66.459 * Pseudo R-squared: 0.005760 * Converged: True * Covariance Type: nonrobust * LLR p-value: 0.6286 * Intercept: * coef: -0.2667 * stderr: 0.300 * z: -0.889 * P>|z|: 0.374 * [0.025 0.975]: -0.854, 0.321 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tnumeric::multi_attribute]]: * coef: -0.2009 * stderr: 0.415 * z: -0.484 * P>|z|: 0.629 * [0.025 0.975]: -1.015, 0.613 * Effect of subject with only the conditions [relational] * Current function value: 0.683177 * Optimization terminated successfully * Function evaluations: 10 * Gradient evaluations: 11 **Result 6:** * Dep. Variable: respondent scores * No. Observations: 90 * Model: Logit DI Model * Date: Tue, 04 Jun 2024 * Log Likelihood: -67.978 * Pseudo R-squared: 0.001884 * Converged: True * Covariance Type: nonrobust * LLR p-value: 0.6390 * Intercept: * coef: -0.2281 * stderr: 0.261 * z: -0.874 * P>|z|: 0.382 * [0.025 0.975]: -0.742, 0.286 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tnumeric::multi_attribute]]: * coef: 0.0161 * stderr: 0.452 * z: 0.037 * P>|z|: 0.971 * [0.025 0.975]: -0.874, 0.907 * Effect of condition with only the conditions [categorical, multi_attribute] for human subjects * Current function value: 0.688033 * Optimization terminated successfully * Function evaluations: 11 * Gradient evaluations: 11 **Result 7:** * Dep. Variable: respondent scores * No. Observations: 116 * Model: Logit DI Model * Date: Tue, 04 Jun 2024 * Log Likelihood: -78.306 * Pseudo R-squared: 0.006407 * Converged: True * Covariance Type: nonrobust * LLR p-value: 0.001537 * Intercept: * coef: 0.0115 * stderr: 0.292 * z: 0.039 * P>|z|: 0.969 * [0.025 0.975]: -0.561, 0.584 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tnumeric::multi_attribute]]: * coef: -1.2887 * stderr: 0.397 * z: -3.245 * P>|z|: 0.001 * [0.025 0.975]: -2.065, -0.512 * Effect of condition with only the conditions [categorical, multi_attribute] for model * Current function value: 0.686076 * Optimization terminated successfully * Function evaluations: 10 * Gradient evaluations: 11 **Result 8:** * Dep. Variable: respondent scores * No. Observations: 78 * Model: Logit DI Model * Date: Tue, 04 Jun 2024 * Log Likelihood: -54.545 * Pseudo R-squared: 0.001876 * Converged: True * Covariance Type: nonrobust * LLR p-value: 0.6510 * Intercept: * coef: 0.2007 * stderr: 0.318 * z: 0.631 * P>|z|: 0.528 * [0.025 0.975]: -0.422, 0.824 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tnumeric::multi_attribute]]: * coef: 0.2549 * stderr: 0.453 * z: 0.562 * P>|z|: 0.573 * [0.025 0.975]: -0.631, 1.140 * Effect of condition with only the conditions [numeric, numeric, multi_attribute] for human subjects * Current function value: 0.688037 * Optimization terminated successfully * Function evaluations: 11 * Gradient evaluations: 11 **Result 9:** * Dep. Variable: respondent scores * No. Observations: 118 * Model: Logit DI Model * Date: Tue, 04 Jun 2024 * Log Likelihood: -80.577 * Pseudo R-squared: 0.0006427 * Converged: True * Covariance Type: nonrobust * LLR p-value: 0.3029 * Intercept: * coef: 0.3796 * stderr: 0.255 * z: 1.487 * P>|z|: 0.137 * [0.025 0.975]: -0.121, 0.881 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tnumeric::multi_attribute]]: * coef: -0.2705 * stderr: 0.386 * z: -0.701 * P>|z|: 0.483 * [0.025 0.975]: -1.028, 0.487 * Effect of condition with only the conditions [numeric, numeric, multi_attribute] for model * Current function value: 0.688130 * Optimization terminated successfully * Function evaluations: 11 * Gradient evaluations: 11 **Result 10:** * Dep. Variable: respondent scores * No. Observations: 78 * Model: Logit DI Model * Date: Tue, 04 Jun 2024 * Log Likelihood: -55.452 * Pseudo R-squared: 0.0007226 * Converged: True * Covariance Type: nonrobust * LLR p-value: 0.3707 * Intercept: * coef: 0.2007 * stderr: 0.318 * z: 0.631 * P>|z|: 0.528 * [0.025 0.975]: -0.422, 0.824 * C[subject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[TClaude::Cisubject_type, Treatment/reference=d[Tnumeric::multi_attribute]]: * coef: -0.1344 * stderr: 0.498 * z: -0.270 * P>|z|: 0.787 * [0.025 0.975]: -1.112, 0.843 * Effect of condition with only the conditions [numeric, multi_attribute] * Current function value: 0.688037 * Optimization terminated successfully * Function evaluations: 11 * Gradient evaluations: 11 ### Key Observations * The models use different combinations of subject types and treatment references. * The LLR p-values vary across the models, indicating different levels of statistical significance. * The coefficients and their significance levels vary, suggesting different impacts of the conditions on the dependent variable. * Most models converged successfully. ### Interpretation The Logit Regression Results provide insights into the relationships between different conditions and respondent scores. The varying LLR p-values suggest that some models are better at explaining the variance in the dependent variable than others. The coefficients indicate the direction and magnitude of the effect of each condition on the respondent scores. The analysis helps in understanding the impact of different factors on the outcome being studied. The models explore different combinations of subject types and treatment references, allowing for a comprehensive understanding of the data.