The independent variables were measured using nominal scale whereas the dependent variable was measured using ordinal scale.
Dear Raphael,
You need to be careful with language here. Influence might imply causation for some people, which you cannot show without something like a randomized control trial.
I agree with Abdulrazzak's advice in most circumstances. Chi-sqaured is a test of association for categorical variables , not of causation or influence. However it only works with one DV and one IV at a time, so you would need to manage the risk of Type I errors, maybe by using a Bonferroni correction to adjust your significance levels.
If your independent variables are binary then you might be able to use ordinal logistic regression with all your IVs and one DV. Alternatively, you might be able to run an explanatory factor analysis and a reliability analysis to turn them into one or more scale variables. The same might apply to your DVs if they are measuring similar things.
Mutivariate analysis are not suitable for ordinal data. The best in your case and because of having the lowest scales (nominal and ordinal scales) is to conduct elaboration of variables.
Keep in mind that elaboration of variables is a causal analysis in which you test a relation between two variables after you introduce control variable(s) as test factors using Chi- Square test.
Elaboration of variables (Crosstabs with control variable(s)) needs sophistication, knowledge and expertise. The results are surprising. With elaboration you get a separate cross-tab for each category of the control variable(s).
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