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I am trying to work on my quantitative method. I took basic OLS regession, and now I am reading basic econometrics which cover experiments, regression, instrumental variables, and differences-in-differences. In what topics  should I go beyond these? I am thinking of looking into time-series analysis. Really appreciate if any quantitative folk can give me a list of essential quantitative topics I should cover. Also, my statistical skills are limited to basic probability, variability. Do you guys think taking casual inferences from pure statistical field would be helpful to advance on my quant method?

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Are you in grad school right now or not?

It sounds like you have your good basic bases covered. If you want to really gain advanced quantitative methods and understand it (which it sounds like you do), I think the next logical step is to actually learn some calculus and maybe linear algebra. Calc is the bases for regression, probability, and is used heavily in game theory and formal modelling.

Time series is kinda hard and also relies on calculus.

More topics you can potentially get into: Bayesian stats, data science principles, different kinds of regression (logit, probit, lasso, etc), nonparametric stats

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Are you in grad school right now or not?

It sounds like you have your good basic bases covered. If you want to really gain advanced quantitative methods and understand it (which it sounds like you do), I think the next logical step is to actually learn some calculus and maybe linear algebra. Calc is the bases for regression, probability, and is used heavily in game theory and formal modelling.

Time series is kinda hard and also relies on calculus.

More topics you can potentially get into: Bayesian stats, data science principles, different kinds of regression (logit, probit, lasso, etc), nonparametric stats

Thanks @eggsala14.  Yeah, I am a second year grad student. I actually contemplate on going back to basic stats before moving into advanced quant. Though i have done decent job on basic ols regression, I dont think i can move beyond that without strong base of stats.

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What does your definition of OLS entail? Have you done hypothesis testing? Interaction terms?

Diagnostics (like VIF, collinearity, leverage)?

Multiple regression?

Strategies for choosing the best model (ie stepwise comparison)?

Basic stats for freshmen will probably be easy for you. If a lot of what I said above is unfamiliar, a first regression course in a stats sequence would be appropriate

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ols = ordinary least squared

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I know that, but what topics are entailed in OLS?

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Causality and probability, random variables, hypothesis testing, univariate, bivariate, and multivariate analysis, dummy variables, and regression assumptions.

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So what exactly is your question?

If you want "essential quant topics" to cover, I need to know more about what your goals with them are. There's a lot going on in the quant side of political science (not to mention all the stuff going on in statistics), so it helps to know whether you're just trying to learn enough to have an idea of what's statistically going on in Political Science, or if you're trying to learn enough to run these statistical methods on your own, or if you're trying to learn enough to become Gary King.

About a causal inference course, all I can say is you should take it if you can. Is it a course in the statistics department? If so, you may need to learn some other math and stats before you'll be qualified to be in it.

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Thanks @eggsalad14. My main goal is to have advanced statistical methods so I can work my research. Personally, I dont believe in cookies cutter approach in which I can just plug data into a statistical software and hope for a significant result. I aim to understand all the nut and bolt logic behind whatever statistical methods I am using,. Now becoming Gary King would be far-fetched for me, considering I dont have genuine interest in methodology, so basically to have strong grip on quant methodology, so I can confidently analyze data and explain my results.

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