Model Fit Details
The Model Fit Details section in the Causal Treatment model report contains two subsections: Treatment Model and Response Model. The contents of these sections differ depending on treatment type.
Binary Treatment
Treatment Model
When the treatment is binary and a treatment model is not specified (REGADJ estimation) in the Fit Model launch window, the Treatment Model section is empty. If a treatment model is specified (IPWR or AIPW estimation), the Treatment Model section contains the Propensity Score Calculation for Treatment tab. In addition, if stabilized weights are used, the Treatment Model section also contains a Propensity Score Null Model tab.
The Propensity Score Calculation for Treatment tab shows information about the fitted treatment model, which is a logistic regression. The information in this section is equivalent to the report that is produced by running the Generalized Linear Mixed Modeling (GLMM) personality with default settings, the treatment variable as the outcome, and the specified treatment model variables as fixed effects. The information in this report shows how the conditional probability of receiving treatment given covariates (that is, the propensity score) is modeled. For a detailed description of all components in a GLMM report, see “Model Fit Reports”. The Propensity Score Null Model tab shows information about the null treatment model, which is a logistic regression. The information in this section is equivalent to the report that is produced by fitting a GLMM with default settings, the treatment variable as the outcome, and no variables included as effects. The information in this report shows how the marginal probability of receiving treatment is modeled. This probability is used in the calculation of stabilized weights.
Response Model
When the treatment is binary and a response model is not specified (IPWR estimation) in the Fit Model launch window, the Response Model section contains two tabs: Propensity Score Weighted Model for ATE and Propensity Score Weighted Model for ATET. If a response model is specified (REGADJ or AIPW estimation), the Response Model section contains two Regression Adjustment Model tabs, one for each level of treatment.
The Propensity Score Weighted Model for ATE tab shows information about the fitted response model, which is a linear or logistic regression. The information in this section is equivalent to the report that is produced by fitting a GLMM with default settings, the response variable as the outcome, the treatment variable as a fixed effect, and the calculated IPW as the weight. The information in this report shows how the ATE is estimated.
The Propensity Score Weighted Model for ATET tab shows information about the fitted response model. The model is a linear or logistic regression fit using only observations that received treatment. After filtering the sample to these observations, the information in this section is equivalent to the report that is produced by fitting a GLMM with default settings, the response variable as the outcome, the treatment variable as a fixed effect, and the calculated IPW for the ATET as the weight. The information in this report shows how the ATET is estimated.
The Regression Adjustment Model tabs show information about the fitted response model. This model is a linear or logistic regression fit that uses only observations that receive the specified level of treatment. After filtering the sample to these observations, the information in these sections is equivalent to the report that is produced by fitting a GLMM with default settings, the response variable as the outcome, and the specified response model covariates as fixed effects.
Censoring Weight Calculation
When the treatment is binary, a treatment model is specified (IPWR or AIPW estimation), and there are missing values in the outcome variable (Y), the Censoring Weight Calculation section contains four tabs.
The Censor Model: Treatment = 1 and Censor Model: Treatment = 0 tabs contain information about the fitted censoring models. These models are fit automatically. The models are logistic regressions that are fit by using only observations that receive the specified level of treatment. After filtering the sample to these observations, the information in these sections is equivalent to the report that is produced by fitting a GLMM with default settings, the indicator that Y is missing as the outcome, and the specified treatment model covariates as fixed effects.
The Censor Null Model: Treatment = 1 and Censor Null Model: Treatment = 0 tabs show information about the fitted censoring models. These models are fit automatically. The models are logistic regressions that are fit by using only observations that receive the specified level of treatment. After filtering the sample to these observations, the information in these sections is equivalent to the report that is produced by fitting a GLMM with default settings, the indicator that Y is missing as the outcome, and no fixed effects.
See Statistical Details for Missing Values in the Outcome for information about how the censoring model affects the final causal effect estimates.
Continuous Treatment
Treatment Model
When the treatment is continuous, a treatment model must be specified. The Treatment Model section contains the Propensity Score Calculation for Treatment tab and a Propensity Score Null Model tab.
The Propensity Score Calculation for Treatment tab shows information about the fitted treatment model, which is a linear regression. The information in this section is equivalent to the report that is produced by fitting a GLMM with default settings, the treatment variable as the outcome, and the specified treatment model variables as fixed effects. The information in this report shows how the conditional density of treatment given covariates (that is, the propensity score) is modeled.
The Propensity Score Null Model tab shows information about the null treatment model, which is a linear regression. The information in this section is equivalent to the report that is produced by fitting a GLMM with default settings, the treatment variable as the outcome, and no variables included as effects. The information in this report shows how the marginal density of treatment is modeled. This density is used in the calculation of stabilized weights.
Response Model
When the treatment is continuous, the Response Model section contains the Marginal Structural Model with SIPW (stabilized inverse probability weighting) tab and the Generalized Propensity Score Model tab.
The Marginal Structural Model with SIPW tab shows information about the response model fit using the MSM with IPWR technique, which is a weighted linear or logistic regression. The information in this section is equivalent to the report that is produced by fitting a GLMM with default settings, the response variable as the outcome, the treatment variable and its square as fixed effects, and the calculated IPW as the weight. See Statistical Details for Continuous Treatment Methods for more information about this model.
The Generalized Propensity Score Model tab shows information about the response model fit using the GPS technique, which is a linear or logistic regression. The information in this section is equivalent to the report that is produced by fitting a GLMM with default settings, the response variable as the outcome, and the treatment variable, its square, the calculated GPS (automatically saved as Observed GPS in the data table), its square, and the interaction between the treatment and the calculated GPS as fixed effects (Hirano and Imbens 2005). See Statistical Details for Continuous Treatment Methods for more information about this model.
The information in the Response Model section for continuous treatment shows how potential outcome means are calculated using the two different modeling techniques.
Censoring Weight Calculation
When the treatment is continuous, censoring weights are not calculated and this section is empty. However, observations with missing values in the outcome are still included in the propensity score estimation.