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Why do Europeans Migrate to Berlin? SocialStructural Differences ...

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12 Verwiebe<br />

regressions is always complex, due <strong>to</strong> the reference categories both in<br />

dependent and independent variables. The dependent variable reasons<br />

for migration has four categories. Multinomial logistic regression calculates<br />

for each category of y the corresponding regression coefficients<br />

b (1) , b (2) , b (3) , b (4) . Thus, mathematically, the multinomial logistic<br />

regression can be defined in the following manner (Greene 2000: 859):<br />

P(y ¼ 1Þ ¼e Xbð1Þ =ðe Xbð1Þ þ e Xbð2Þ þ e Xbð3Þ þ 1Þ<br />

P(y ¼ 2Þ ¼e Xbð2Þ =ðe Xbð1Þ þ e Xbð2Þ þ e Xbð3Þ þ 1Þ<br />

P(y ¼ 3Þ ¼e Xbð3Þ =ðe Xbð1Þ þ e Xbð2Þ þ e Xbð3Þ þ 1Þ<br />

P(y ¼ 4Þ ¼1=ðe Xbð1Þ þ e Xbð2Þ þ e Xbð3Þ þ 1Þ<br />

The coefficients b (1) (solely social reasons), b (2) (solely economic reasons),<br />

b (3) (solely cultural reasons), measure the relative differences<br />

against the reference category y = 4 (mixed reasons). This reference category<br />

was chosen for content-related reasons: the theoretical debate is<br />

mainly organised around a discussion of the relevance of economic and<br />

social reasons, but recently cultural reasons have also been given some<br />

attention. Mathematically, a different reference category for the dependent<br />

variable <strong>do</strong>es not change the results of the model. The exponential<br />

value (odds ratio) of the parameters b can be used for the interpretation<br />

of the results. They refer <strong>to</strong> the risk ⁄ chance of an event occurring. These<br />

odds ratios always take values > 0. A positive effect of the odds ratios<br />

is expressed as e b >1, a negative effect as e b

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