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I'm a forth year economics student (undergraduate) and last semester I wrote a research paper, with a classmate, in which we analyzed the determinants of interprovincial migration flows in Canada. It was for an applied econometrics class. We used a generalized gravity model with random-effects, and the GLS method to estimate the parameters (we found first-order autocorrelation).

The model (which I've included below, along with a link to the paper) performed well in terms of the statistical significance of terms (11 out of 16 at $p<0.01$), $R^2$ values, et cetera. However, when I used a multiple regression quadratic assignment procedure (MRQAP), the only statistically significant terms were the population sizes of the source and destination provinces. I'm wondering if someone might be able to explain to me the possible reasons for such a result.

My inspiration for trying out a MRQAP approach was the paper International Migration: A Global Complex Network. I used Stata. I didn't use the results of the MRQAP in the paper, given that I don't fully understand it, but I am curious nonetheless.

I do understand that MRQAP analysis is used for dyadic data that might exhibit network dependencies. What I'm looking for is just an explanation, in relatively non-technical terms, of what might be going on in this particular context. That might look something like: the majority of net interprovincial migration is only between a few provinces, which skews your results in a manner that is apparent when using MRQAP, but not GLS.

The exact model we used is:

\begin{align*} \log{(M_{ijt})} &= \beta_0 + \beta_1 \log{(GDPpc_{it})} + \beta_2 \log{(GDPpc_{jt})} + \beta_3 \log{(dist_{ij})} \\ &+ \beta_4 \log{(pop_{it})} + \beta_5 \log{(pop_{jt})} + \beta_6 \log{(grads_{it})} + \beta_7 \log{(grads_{jt})} \\ &+ \beta_8 popshare_{it} + \beta_9 border_{ij} + \beta_{10} \log{(UE_{it})} + \beta_{11} \log{(UE_{jt})} \\ &+ \beta_{12} \log{(CPI_{it})} + \beta_{13} \log{(CPI_{jt})} + \beta_{14} newhouse_{it} \\ &+ \beta_{15} newhouse_{jt} + \beta_{16} wage_{jt} \end{align*}

The subscripts $i$ and $j$ indicate the source and destination province, respectively. Migration between province $i$ and $j$ at year $t$ is given by $M_{ijt}$. For more detailed information, the actual paper is here.

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    $\begingroup$ Without digging into your paper and the theories behind it, my guess is your observations are not independent. Most regression models assume independent observations, unless you explicitly model that clustering. QAP regression is designed to model social network data, which are by definition inter-dependent. So an explanation for why your coefficients are no longer significant is that the QAP model is accounting for clustering of migrants, which from a quick read of gravity theory would be expected. Are your point estimates changing or just your standard errors? $\endgroup$ – robin.datadrivers Jan 17 '15 at 3:05
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I think robin.datadrivers response is correct. You should have used multiple regression analysis instead and identify the significant correlations between your dependent variables.

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