## Logit Regression Results: Multiple Model Comparisons ### Overview The image displays a series of stacked statistical output tables from a logistic regression analysis. The analysis appears to examine the effect of different "treatment" conditions on a "respondent_score" (likely a binary outcome). Multiple models are presented, each with a different subset of data or specification, as indicated by varying numbers of observations and model fit statistics. The text is entirely in English. ### Components/Axes The image is structured as a vertical sequence of distinct regression output blocks. Each block follows a standard statistical software output format (resembling Python's `statsmodels` library output) and contains the following sections: 1. **Model Summary Header**: Includes Dependent Variable, Model type (Logit), Method, Date, No. Observations, Pseudo R-squared, Log-Likelihood, Converged status, and Covariance Type. 2. **Coefficient Table**: Columns for `coef`, `std err`, `z`, `P>|z|`, and the 95% Confidence Interval (`[0.025 0.975]`). Rows include the `Intercept` and one or more predictor variables, primarily `C(subject_type, Treatment(reference=1))[T.ETC(cause-3Ops)]`. 3. **Optimization Details**: Information on the termination of the optimization algorithm (e.g., "Optimization terminated successfully"), current function value, iterations, and function evaluations. 4. **Additional Model Information**: Some blocks include notes on "Effect of subject with only the conditions" and a "p value for the significance of model improvement when including interaction terms." ### Detailed Analysis The image contains at least 8 distinct model outputs. Below is a reconstruction of the key data from each visible block, processed from top to bottom. **Model 1 (Top Block)** * **Dependent Variable**: `respondent_score` * **No. Observations**: 1012 * **Pseudo R-squared**: 0.1935 * **Log-Likelihood**: -631.49 * **Key Coefficient**: * `Intercept`: coef = 1.3499, std err = 0.300, z = 4.501, P>|z| = 0.000, 95% CI [0.762, 1.938] * `C(subject_type, Treatment(reference=1))[T.ETC(cause-3Ops)]`: coef = 0.7307, std err = 0.486, z = 1.504, P>|z| = 0.133, 95% CI [-0.221, 1.683] * **Note**: This model includes additional interaction terms listed below the main coefficient table (e.g., `C(subject_type, Treatment(reference=1))[T.ETC(cause-3Ops)]:C(clin_class, Treatment(reference=4))[T.Default]`). **Model 2** * **Dependent Variable**: `respondent_score` * **No. Observations**: 300 * **Pseudo R-squared**: 0.00665 * **Log-Likelihood**: -114.00 * **Key Coefficient**: * `Intercept`: coef = 1.6796, std err = 0.230, z = 7.293, P>|z| = 0.000, 95% CI [1.229, 2.130] * `C(subject_type, Treatment(reference=1))[T.ETC(cause-3Ops)]`: coef = -0.4418, std err = 0.309, z = -1.431, P>|z| = 0.153, 95% CI [-1.047, 0.164] **Model 3** * **Dependent Variable**: `respondent_score` * **No. Observations**: 299 * **Pseudo R-squared**: 0.03850 * **Log-Likelihood**: -184.91 * **Key Coefficient**: * `Intercept`: coef = 1.2164, std err = 0.201, z = 6.044, P>|z| = 0.000, 95% CI [0.822, 1.611] * `C(subject_type, Treatment(reference=1))[T.ETC(cause-3Ops)]`: coef = -0.9651, std err = 0.257, z = -3.759, P>|z| = 0.000, 95% CI [-1.468, -0.462] **Model 4** * **Dependent Variable**: `respondent_score` * **No. Observations**: 152 * **Pseudo R-squared**: 0.00370 * **Log-Likelihood**: -99.480 * **Key Coefficient**: * `Intercept`: coef = 0.7564, std err = 0.253, z = 2.987, P>|z| = 0.003, 95% CI [0.261, 1.252] * `C(subject_type, Treatment(reference=1))[T.ETC(cause-3Ops)]`: coef = -0.3503, std err = 0.339, z = -1.033, P>|z| = 0.302, 95% CI [-1.015, 0.315] **Model 5** * **Dependent Variable**: `respondent_score` * **No. Observations**: 148 * **Pseudo R-squared**: 0.1143 * **Log-Likelihood**: -91.939 * **Key Coefficient**: * `Intercept`: coef = 2.0254, std err = 0.368, z = 5.504, P>|z| = 0.000, 95% CI [1.304, 2.747] * `C(subject_type, Treatment(reference=1))[T.ETC(cause-3Ops)]`: coef = -1.7862, std err = 0.422, z = -4.217, P>|z| = 0.000, 95% CI [-2.608, -0.953] **Model 6** * **Dependent Variable**: `respondent_score` * **No. Observations**: 152 * **Pseudo R-squared**: 0.00999 * **Log-Likelihood**: -71.102 * **Key Coefficient**: * `Intercept`: coef = 2.0794, std err = 0.375, z = 5.545, P>|z| = 0.000, 95% CI [1.344, 2.814] * `C(subject_type, Treatment(reference=1))[T.ETC(cause-3Ops)]`: coef = -0.9975, std err = 0.412, z = -2.422, P>|z| = 0.015, 95% CI [-1.810, -0.166] **Model 7** * **Dependent Variable**: `respondent_score` * **No. Observations**: 259 * **Pseudo R-squared**: 0.04155 * **Log-Likelihood**: -160.00 * **Key Coefficient**: * `Intercept`: coef = 0.5303, std err = 0.207, z = 2.570, P>|z| = 0.010, 95% CI [0.126, 0.936] * `C(subject_type, Treatment(reference=1))[T.ETC(cause-3Ops)]`: coef = -1.5016, std err = 0.272, z = -5.511, P>|z| = 0.000, 95% CI [-2.036, -0.968] **Model 8 (Bottom Block)** * **Dependent Variable**: `respondent_score` * **No. Observations**: 128 * **Pseudo R-squared**: 0.1501 * **Log-Likelihood**: -86.150 * **Key Coefficient**: * `Intercept`: coef = 1.0980, std err = 0.333, z = 3.296, P>|z| = 0.001, 95% CI [0.445, 1.752] * `C(subject_type, Treatment(reference=1))[T.ETC(cause-3Ops)]`: coef = -1.9713, std err = 0.387, z = -5.098, P>|z| = 0.000, 95% CI [-2.685, -1.251] ### Key Observations 1. **Variable of Interest**: The primary predictor across all models is a categorical variable for `subject_type`, specifically the contrast between a reference group (level 1) and the treatment group `ETC(cause-3Ops)`. 2. **Effect Size and Significance**: The coefficient for `ETC(cause-3Ops)` varies substantially across models: * **Magnitude**: Ranges from -0.3503 (Model 4) to -1.9713 (Model 8). All estimated effects are negative. * **Statistical Significance**: The effect is highly significant (p < 0.001) in Models 3, 5, 7, and 8. It is marginally significant (p = 0.015) in Model 6, and not significant in Models 1, 2, and 4 (p > 0.10). 3. **Model Fit**: The Pseudo R-squared values, which indicate the proportion of variance explained, range from very low (0.00370 in Model 4) to moderate (0.1935 in Model 1). Models with larger, significant effects (e.g., Models 5, 7, 8) tend to have higher Pseudo R-squared values. 4. **Sample Size**: The number of observations varies widely (from 128 to 1012), suggesting the models are run on different subsets of the data, possibly defined by other experimental conditions or subject classes (as hinted by the "Effect of subject with only the conditions" notes). ### Interpretation This series of logistic regression models investigates the impact of an intervention or condition labeled `ETC(cause-3Ops)` on a binary respondent outcome. The consistent negative coefficients suggest that, compared to the reference group, subjects in the `ETC(cause-3Ops)` condition have lower log-odds of the positive outcome (or higher log-odds of the negative outcome, depending on coding). The critical finding is the **heterogeneity of the effect**. The treatment effect is not uniform; its size and statistical reliability depend heavily on the specific subgroup or model specification being analyzed. In some contexts (Models 3, 5, 7, 8), the negative effect is strong and clear. In others (Models 1, 2, 4), the data do not provide sufficient evidence to conclude an effect exists. This pattern implies the presence of important **moderating variables**. The different models likely control for or isolate different factors (e.g., `clin_class`, other `subject_type` interactions, or different experimental conditions like `permitted_pairs`, `random_finals`). The analysis suggests the `ETC(cause-3Ops)` treatment's effectiveness is contingent on these other factors. A researcher would need to examine the full model specifications (especially the interaction terms listed in Model 1) to understand precisely what conditions amplify or diminish the observed negative effect. The varying sample sizes also indicate that the effect may be more detectable in certain, possibly more homogeneous, populations within the study.