Quantitative modeling in social science vs natural science

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soc.scientist
The study of social science phenomena using empirical data such as register data* are very often approached with an regression model.
One of the most used approaches is a linear model where the parameters is estimated with ordinary least squares. The models of
this type is often called OLS-models within this context. A common example could be how income is impacted by marital status. In this example
the dependent variable is income and the independent experimental variable is marital status. Often a set of control variables are included, such as
gender, age, race, and etc. Often the researcher try including different type of control variables and observe how well the model performs by the "regression diagnostics" such as
overall R value, significance values and so on. This type of basic model and modeling work is very common within social science research.
This methodology is introduced for social science students and very little information of the math behind the models is taught. The linear "OLS"
model is the workhorse and alternative approaches are almost not even mentioned. In several books that are used in statistics courses at Ph.D student level
in social sciences for instance calculus and differential equations are not even mentioned.

In contrast, students that study a master of science in engineering are in the first semester introduced to calculus and differential equations and the approach
to model a phenomon is fundamently different (of course the phenomena are different so different approaches are likely needed) but the whole idea of
modeling is different. When I studied engineering I did not heard a single word about regression models. Instead, the approach we were taught was to
observe the data and try if the data could be fitted by a power function, exponential function, linear function, etc. or a combination of functions.

I guess my forum post boils down to this question: Why are social science students taught regression modeling without even mentioning for instance differential equations
which could be regarded as the workhorse of many natural and technical sciences? (Some social science Ph.Ds havent heard about Fourier Series, not to mention Laplace transforms...)


*note: register data is in this context is official data recorded and prepared by national statistics offices like "Statistics Sweden" or other similar office or agency.
 

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The first and most obvious answer is that most students of social science don't do any modelling for which differential equations would be appropriate; regression models are far more useful for most of their purposes. The second reason is that most social science students (unfortunately) don't study enough mathematics to know what a differential equation is, let along how to set one up or solve one.

Instead, the approach we were taught was to
observe the data and try if the data could be fitted by a power function, exponential function, linear function

That's essentially regression.

Some social science Ph.Ds havent heard about Fourier Series, not to mention Laplace transforms...

Neither have most music Ph.D's; largely because they have no need for them.
 
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There is no shortage of quantitative firepower in the social sciences, would refer you to the Santa Fe institute, for example. You cannot escape fourier series, hermite polynomials and all sorts of transforms when dealing with aspects of continuous probability distributions

Physics is essentially far simpler than social sciences as in physics you are dealing with fundamental entities - forces, particles etc. that have deterministic laws that govern their behavior. Where you have randomness either in quantum mechanics or in statistical mechanics probabilities can generally be accurately calculated. While statistics is used heavily in social sciences, they are used to estimate uncertainty related to the actions of individuals

almost a century ago, Frank Knight pointed out the problem of uncertainty as differentiated from probabilistic risk. One can accurately calculate odds of particular outcomes in a casino, you cannot do the same in real life

The liability of opinion or estimate to error must be radically distinguished from probability or chance of either type, for there is no possibility of forming in any way groups of instances of sufficient homogeneity to make possible a quantitative determination of true probability. Business decisions, for example, deal with situations which are far too unique, generally speaking, for any sort of statistical tabulation to have any value for guidance. The conception of an objectively measurable probability or chance is simply inapplicable

there is a good book by physicist turned wall street quant Emanuel Derman on this topic. While he more specifically talks about finance, his points apply to all social sciences.

There is a review here: http://mathbabe.org/2011/10/25/emanuel-dermans-models-behaving-badly/

The similarity of physics and finance lies more in their syntax than their semantics. In physics you’re playing against God, and He doesn’t change His laws very often. In finance you’re playing against God’s creatures, agents who value assets based on their ephemeral opinions. The truth therefore is that there is no grand unified theory of everything in finance. There are only models of specific things.
 

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