Merge branch 'bl-ch1'

_posts/2024-05-12-experimental-survey-designs.md

@@ -21,9 +21,9 @@ Notes for Chapter 2 of [Causal Inference with Survey Data](https://www.linkedin.
 | ----- | ----- | ------- |
 | Simple randomization  | Assigns equal probability to treatment and control groups |- Easy to implement<br>- Can lead to unequal group sizes in small trials |
 | Block randomization  | Get similar group sizes by dividing subjects into predetermined number of subjects (often a multiple of the number of groups, like 4, 8, etc. for two groups). Within each block, participants are then randomly assigned to treatment groups.  |- Requires choosing the total number of subjects in each block <br>- Can often avoid imbalance in small trials seen with simple randomization |
-| Stratified randomization  | Balance based on characteristics/covariates (like age, sex, etc.) before randomizing within these strata |<ul><li>Ensures balance in important covariates between groups  |
+| Stratified randomization  | Balance based on characteristics/covariates (like age, sex, etc.) before randomizing within these strata |- Ensures balance in important covariates between groups  |
 | Cluster randomization  | Randomizes entire groups (like schools or hospitals) |- Suitable for group-level interventions or when individual assignment is impractical   |
-| Covariate adaptive randomization  | Increases the probability of being assigned to a group to address a deficit of a particular characteristic   within the group |<ul><li>Effective in trials with small sample sizes or multiple important covariates |
+| Covariate adaptive randomization  | Increases the probability of being assigned to a group to address a deficit of a particular characteristic within the group |- Effective in trials with small sample sizes or multiple important covariates |
 
 - Before randomization, the number of observations is typically calculated ahead of time based on a specific effect size (power analysis). You need to consider measure of variability (standard deviation), significance level, and power.
 - You can make a graph of sample size on y-axis and effect size on x-axis to see the relationship.

_posts/2024-05-16-cross-sectional-survey-designs.md

@@ -0,0 +1,197 @@
+---
+title: "Cross-Sectional Survey Designs"
+mathjax: true
+toc: true
+toc_sticky: true
+categories: [data science, statistics]
+---
+
+Notes for Chapter 3 of [Causal Inference with Survey Data](https://www.linkedin.com/learning/causal-inference-with-survey-data/surveys-with-cross-sectional-data?autoSkip=true&resume=false&u=185169545) on LinkedIn Learning, given by Franz Buscha. I'm using this series of posts to take some notes.
+
+
+```python
+import graphviz as gr
+```
+
+
+```python
+def draw_causal_graph(
+    edge_list, node_props=None, edge_props=None, graph_direction="UD"
+):
+    """Utility to draw a causal (directed) graph
+    Taken from: https://github.com/dustinstansbury/statistical-rethinking-2023/blob/a0f4f2d15a06b33355cf3065597dcb43ef829991/utils.py#L52-L66
+
+    """
+    g = gr.Digraph(graph_attr={"rankdir": graph_direction})
+
+    edge_props = {} if edge_props is None else edge_props
+    for e in edge_list:
+        props = edge_props[e] if e in edge_props else {}
+        g.edge(e[0], e[1], **props)
+
+    if node_props is not None:
+        for name, props in node_props.items():
+            g.node(name=name, **props)
+    return g
+```
+
+# Cross-sectional survey designs
+
+- It's a snapshot in time, capturing information from many subjects.
+- Most common type of survey.
+
+**Examples**
+1. Census surveys. Provides a snapshot of a country's population (e.g. US Census done every 10 years).
+1. Expenditure surveys. Information on buying habits (e.g. annual Consumer Expenditure Survey).
+1. Labor force surveys. Collect data on employment (e.g. UK Labour Force Survey, conducted quarterly).
+
+**Advantages**
+- Availability
+- Cheap to conduct
+- Versatility in topics
+
+**Disadvantages**
+- Lack temporal data
+- Sampling, selection, and response bias
+- Lack of depth (limited data on complex issues)
+
+**Statistical Framework**
+- A key to working with cross-sectional data is the $i$ subscript, such as in the form:
+
+$$ Y_i = \beta_0 + \beta_1X1_i + \beta_2X2_i + ... \epsilon_i$$
+
+- The $i$ denotes different observations in the data (e.g. subjects or entities at a single point in time)
+
+**Conclusion**
+- Broad application and more themes.
+- Explanatory variables must be used in innovative ways for cause-and-effect analysis.
+
+# Regression analysis
+
+- A fundamental statistical method
+- A powerful tool for controlling observable factors
+- Mainstay of causal analysis
+
+**DAG: Controlling for Observable Factors**
+
+- A regression model can answer this question: What is the causal effect of X on Y?
+
+
+
+
+```python
+draw_causal_graph(
+    edge_list=[("X1i", "Yi"), ("ε", "Yi")],
+    edge_props={("ε", "Yi"): {"style": "dashed", "label": "β"}},
+    graph_direction="LR",
+)
+```
+
+
+
+
+
+![svg](/assets/2024-05-16-cross-sectional-survey-designs_files/2024-05-16-cross-sectional-survey-designs_6_0.svg)
+
+
+
+
+Other factors that are not seen in the survey data are summed up in the hidden error term.
+
+$ Y_i = \beta_0 + \beta_1X1_i + \epsilon_i $
+
+- Regression can control for many observable factors
+- Effects estimated in a regression model are independent of other effects in the model
+- Causal infrence relies on there being no confounders (exogeneity assumption)
+- Variables that don't gice a choice are often exogenous (sex, age, parents birthplace, etc.). These are variables that are "hard to influence".
+- Assumption of exogeneity can be difficult. There can be many factors that drive both Y and X1. This creates a backdoor pathway.
+
+
+
+```python
+# `ε` is unicode for epsilon since `ε` fails to render
+draw_causal_graph(
+    edge_list=[("X1i", "Yi"), ("ε", "Yi"), ("ε", "X1i")],
+    edge_props={
+        ("X1i", "Yi"): {"label": "β1"},
+        ("ε", "Yi"): {"style": "dashed"},
+        ("ε", "X1i"): {"style": "dashed", "label": "backdoor"},
+    },
+    graph_direction="LR",
+)
+```
+
+
+
+
+
+![svg](/assets/2024-05-16-cross-sectional-survey-designs_files/2024-05-16-cross-sectional-survey-designs_8_0.svg)
+
+
+
+
+If the backdoor is present, then the estimate of $\beta_1$ will not be correct.
+
+But imagine that $X2i$ in the error term can be observed. A new DAG might look like this.
+
+
+```python
+draw_causal_graph(
+    edge_list=[("X1i", "Yi"), ("ε", "Yi"), ("X2i", "X1i"), ("X2i", "Yi")],
+    edge_props={
+        ("X1i", "Yi"): {"label": "β1"},
+        ("X2i", "Yi"): {"label": "β2"},
+        ("ε", "Yi"): {"style": "dashed"},
+        ("ε", "X1i"): {"style": "dashed", "label": "backdoor"},
+    },
+    graph_direction="LR",
+)
+```
+
+
+
+
+
+![svg](/assets/2024-05-16-cross-sectional-survey-designs_files/2024-05-16-cross-sectional-survey-designs_10_0.svg)
+
+
+
+
+$ Y_i = \beta_0 + \beta_1X1_i + \beta_2X2_i + \epsilon_i $
+
+$X2$ is now specifically controlled for.
+
+Triangular Tables:
+A way to observe the effect on a regression model of incrementally adding more variables but be careful of overfitting. Knowing what variables to include requires some domain knowledge.
+
+**Advantages**
+- Flexibility in variables
+- Many different forms for different data
+- Easy to understand
+
+**Disadvantages**
+- Often too simple
+- Cannot control for unobserved confounders
+
+**Conclusion**
+- Don't dismiss basic regression
+- Underpins more complex models
+- Works well with large surveys and many variables
+
+
+```python
+%load_ext watermark
+%watermark -n -u -v -iv -w
+```
+
+    Last updated: Sun May 19 2024
+
+    Python implementation: CPython
+    Python version       : 3.11.7
+    IPython version      : 8.21.0
+
+    graphviz: 0.20.1
+
+    Watermark: 2.4.3
+
+