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This graduate-level troubleshooting guide supports students across the Los Angeles MSA & San Francisco Bay Area MSA, including UCLA, USC, UC Berkeley, UC Irvine, UC Davis, UC Santa Cruz, UC Riverside & all CSU campuses. It covers Research Theory, Regression Theory & Causal Inference Theory at a deep theoretical level, aligned with graduate programs in economics, statistics, public policy, business analytics & social sciences.
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Information Gain Section
This troubleshooting guide isolates the exact theoretical gaps that cause confusion in graduate research and regression coursework. Each question targets a specific conceptual failure point—identification, endogeneity, sampling assumptions, asymptotics, causal diagrams, or estimator behavior—so you can diagnose errors in your reasoning. The goal is to understand why models behave the way they do, how assumptions shape inference, and how to evaluate whether your research design is theoretically valid.
Research, Regression & Causal Inference Theory FAQ (50 Graduate-Level Questions)
1. What is internal validity?
Internal validity measures whether the research design identifies a causal effect without bias from confounding or design flaws.
2. What is external validity?
External validity concerns whether results generalize beyond the study sample or context.
3. What is the difference between random sampling and random assignment?
Random sampling selects units for study; random assignment allocates treatment within the study.
4. What are the main threats to internal validity?
Confounding, selection bias, measurement error, omitted variables, and reverse causality.
5. What is construct validity?
Construct validity measures whether a variable accurately represents the theoretical concept.
6. What is reliability?
Reliability measures the consistency of a measurement across repeated observations.
7. What is the difference between experimental and observational research?
Experiments manipulate treatment; observational studies rely on naturally occurring variation.
8. What is the counterfactual framework?
Causal effects compare outcomes under treatment vs. control for the same unit, which is unobservable.
9. What is selection bias?
Selection bias occurs when treatment assignment correlates with potential outcomes.
10. What is measurement error?
Measurement error occurs when observed variables differ from true values, biasing estimates.
11. What is classical measurement error?
Error is independent of the true value and other regressors, typically attenuating coefficients.
12. What is nonclassical measurement error?
Error correlates with true values or regressors, producing unpredictable bias.
13. What is sampling variability?
Sampling variability reflects random differences between the sample and population.
14. What is the difference between a parameter and a statistic?
A parameter describes a population; a statistic describes a sample.
15. What is a research hypothesis?
A hypothesis states a testable claim about a population parameter or causal relationship.
16. What is a conceptual framework?
A conceptual framework links theory, variables, and expected relationships.
17. What is triangulation in research?
Triangulation uses multiple methods or data sources to validate findings.
18. What is ecological fallacy?
It occurs when group-level relationships are incorrectly applied to individuals.
19. What is Simpson’s paradox?
A trend reverses when data are aggregated vs. disaggregated due to confounding.
20. What is the difference between mediation and moderation?
Mediation explains how a treatment affects an outcome; moderation changes the strength of the effect.
21. What are the classical OLS assumptions?
Linearity, random sampling, no perfect multicollinearity, zero conditional mean & homoskedasticity.
22. What is the zero conditional mean assumption?
It requires E[u | X] = 0 for unbiased OLS estimates.
23. What is omitted variable bias?
Bias occurs when a relevant variable correlates with both the regressor and the error term.
24. How do I compute omitted variable bias?
Use the formula:
Bias = β₂ * Cov(X₁, X₂) / Var(X₁)
25. What is multicollinearity?
Multicollinearity occurs when regressors are highly correlated, inflating standard errors.
26. What is heteroskedasticity?
Heteroskedasticity occurs when error variance depends on X.
27. What is autocorrelation?
Autocorrelation occurs when errors correlate across time.
28. What is functional form misspecification?
It occurs when the model omits nonlinearities or interactions.
29. What is the Gauss–Markov theorem?
OLS is BLUE under classical assumptions.
30. What is the difference between unbiasedness and consistency?
Unbiasedness concerns finite samples; consistency concerns convergence as n grows.
31. What is the asymptotic distribution of the OLS estimator?
Under standard conditions:
√n (β̂ − β) → 𝒩(0, σ² (X′X)⁻¹)
32. What is maximum likelihood estimation for regression?
MLE chooses parameters that maximize the likelihood of observing the data.
33. What is the likelihood function for linear regression?
Assuming normal errors:
L(β, σ²) ∝ (σ²)⁻ⁿ⸍² exp[−(1∕(2σ²))(Y − Xβ)′(Y − Xβ)]
34. What is regularization?
Regularization penalizes coefficient size to reduce variance.
35. What is ridge regression?
Ridge adds an L2 penalty:
β̂ᵣᵢdᵍₑ = argmin (‖Y − Xβ‖² + λ‖β‖²)
36. What is LASSO?
LASSO adds an L1 penalty, enabling variable selection.
37. What is cross-validation?
Cross-validation evaluates model performance on held-out data.
38. What is model identification?
Identification requires that parameters are uniquely determined by the data-generating process.
39. What is endogeneity?
Endogeneity occurs when regressors correlate with the error term.
40. What is the instrumental variables estimator?
IV isolates exogenous variation using instruments.
41. What is a causal DAG?
A Directed Acyclic Graph encodes causal relationships and identifies confounding paths.
42. What is the backdoor criterion?
A set of variables satisfies the backdoor criterion if conditioning on them blocks all backdoor paths.
43. What is the frontdoor criterion?
It identifies causal effects using mediators when confounding blocks direct identification.
44. What is the difference between confounding and mediation?
Confounders bias causal effects; mediators transmit causal effects.
45. What is the potential outcomes framework?
It defines causal effects as contrasts between potential outcomes under treatment vs. control.
46. What is the ATE?
The Average Treatment Effect is E[Y(1) – Y(0)].
47. What is the LATE?
The Local Average Treatment Effect applies to compliers in IV settings.
48. What is Difference-in-Differences?
DiD identifies causal effects by comparing treated vs. control groups over time.
49. What is Regression Discontinuity?
RD identifies causal effects using a cutoff-based assignment rule.
50. What is synthetic control?
Synthetic control constructs a weighted combination of control units to approximate a counterfactual.
Related Pages
- Research Help
- Statistics
- Mathematical Statistics
- Econometrics
- Biostatistics
- Stata, R & SPSS
- Calculus & Linear Algebra
- Linear Programming
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