Interesting problem.  For your IV problem, if you can use the original measures of income and job security, you might learn more than trying to use the precarity measure with status inconsistency.  But you are correct that you will run into problems using precarity with status inconsistency - it will act like using income twice.  You might get results, but interpreting them will be really challenging.  My instinct would be to try each piece separately, comparing the results empirically, if you have the information.

   For the analysis question, I would probably try an ordered probit model using maximum likelihood estimation.

Thanks for your reply Julia. Maybe it is a good idea to use the original measures. I could also run the analysis with precarity measure to see if it gives anyresults, separately. 

1) your 1-13 scale variable is probably discrete (a score) and not continuous, I guess. But this does not make a strong difference as an independant variable.

2) As your dependent variable is an ordinal categorical variable, yes ordinal regression is a good starting point. « The best » may depend on the structure of the data, and of your exact question.

3) If your two « independant » variables are correlated, they still can be used simultaneously in the model, but that makes interpretations much more difficult, and parameter estimates much less precise.

The question is wether those who are more precair, vote more for the right or extreme-right parties. 

And if there is a difference between several precarity groups. For example in the high income group those with and without job insecurity, and the same for medium and low income group. 

I think I wont use them together in the model, since my statistical knowledge is not that advanced yet. I am currently working on my sociology thesis. 

Rereading your question... I wonder if voting intention is really so ordinal... I mean, left to right is a geographical ordered relationship, but does this sitting convention really reflect a kind of order in different politic ideas? But as I am not a sociologit or politicist, this is just a curiosity question.

You may have easier to interpret coefficients using logit ordinal regression (odds-ratio) than probit ordinal regression, but it also depends on the usage in your community. Results should be close anyway. However, in both cases, dont forget to check that the link between voting and « independent » variable (I prefer « predictor », less confusing) is really linear in the selected scale and symmetrical, otherwise other links may be more suited. Especially, symmetry may be raised since extreme-left may be not so extreme or more extreme from center than extreme-right.

How would I check for this symmetry? 

First of all, let me start out my first point with your identification of independent variables. As far as I am concerned, I have noticed the fact that you are planning to reflect precarity and status inconsistency as independent variables in your model. Yes, I would definitely agree with the point that there is a high possibility of getting in touch with higher effects of colinearity among the status inconsistency and precarity due to the overlapping measurements. I would suggest you to look into the variables in two separate dimensions of testing in the model. I feel that It is good to reflect on the original values of income and job security independently instead of combining them together as it may deal with similar form of meaning. You could also deal with the bootstrapping form of testing in order for you to look into the individual effects of variables. I do agree with the point that the voting system/choice should not be reflected as the ordinal form of variable due to the fact that it doesn't deal with the logical form of statements and it is tied up with the greater variations of political movements. I may not be able to agree with the options that you have selected for the voting choice as it will be bias to the context of reality. You may need to deal with different forms of validations and reliability in terms of construction of model/variables based on the relevant concepts/theories before you can finalize your selected version of variables and you may need to follow up with the systematic flow of questionnaire in order to follow up with the variations of subjectivity among the responses of respondents. In my point of view, I would  clearly reflect the status inconsistency and voting choice as nominal variables due to its capacity of not dealing with logical form of ordering. You may need to think about some mediating/moderating forms of variables that can facilitate the association between income/job security/status inconsistency and voting choice such as level of education, age, cognitive thoughts, levels of trust and fairness(concepts of animal spirits) and etc. After you have finalized all those basic things, then only, you can move on to the real testing of it. After finalization, you may need to deal with the parametric/non-parametric mode of multiple regression if your dependent variable is a continuous variable otherwise, you may just deal with logit/probit form of regression if your dependent variable is a categorical variable(nominal). It depends on the nature of distributions among the variables that you are dealing with. You may need to deal with normality tests first to determine on whether your variables are follow the symmetric form of variation. If it is not normal, then, you may need to identify the approximate fitting of distribution  tests(quadratic/cubic/poisson and etc tests) before you can specify the structure of your model. I can help you with it if you need further explanations or help in analysing your data. I will be very much happy to share my additional thoughts about it with you later when i have the time for it again.Thank you.

Note:

Parametric mode of multiple regression/Probit regression(nominal)/Ordered Probit Regression(Ordinal) = Distribution of residuals should be normal

Non-Parametric mode of multiple regression/Logit regression(nominal)/Ordered Logit Regression(Ordinal)=Distribution of residuals should not be normal and can be free distribution.

Thank you and Happy Learning.

Thanks a lot! Really usefull information. If you have any additional thoughts that would always be welcome.

The main theme of my thesis is if the 'precariat' in belgium is a danger to democracy. This is based on a book from guy Standing I have read, who says that precarity can lead to extreme voting behavior (although in belgium this can also make voting for the right-wing party rise) and to a decline in political participation, or sometimes an increase (like for example euro mayday parade and such). 

So maybe it is best I use a multinomial regression for the voting choice. But first as you said, I need to get my independent variables sorted and see which I am going to include. A normal regression for voting choice is not really going to work, since its a nominal. For my other dependent variable 'political participation' it will work. But I will also devide political participation in 4 groups based on literature (formal, activistic, new (ineternet) and voting yes/no). Formal and activistic are on a scale from 1-5 and 1-6, the other 2 are just yes or not. So no scale for those. But I combine them all except voting to see general political participation. And after that I want to look at each form of participation in itself and how its linked to the measures of precarity.

I have already made up a point that you may need to deal with probit/tobit regression and since your dependent variable/predictand has more than 2 options, then, you may need to deal with multinomial mode of probit/logit regression and please remember that the decision between the selection of multinomial mode of probit/logit regression depends on the nature of distribution among the residuals (the differences between actual values and predicted values) that you are dealing with. Yes, you may need capture the effects of highly correlated predictors on predictand separately and there are many things that can be done to the current context of study. In a way, you are only dealing with nominal variables and no ordinal context of it in your study, Madam. I can share more thought on the similar research issues that you are dealing with later. If you think that precariat is an important, then, you can just capture precariat by adding up additional variables such as trust/fairness of participation and dynamism of virtual mode of political participation through social networks and etc and by ignoring status inconsistency if it doesn't have any important value, Madam. My email address is [email protected]/[email protected] if you need additional inputs from me.  As I said earlier, there are many variables that can be considered for your research to maintain effective flow of intellectual arguments in the research topic that you are covering.

You can also highlight different forms of political changes through the usage of dummy variable/categorical variable and reflect that as a mediator/moderator based on the empirical form that you have referred to, Madam. You could also think about the term of arousal to refer to the psychological state of mind towards the voting choice among the participants and think about other possibilities that can strengthen the intellectual capacity of your thesis.

In line with Emmanuel's comments above, and without any subject knowledge on this field of research, I would like to suggest a few points.

1. There may be a tension between simplicity and statistical efficiency. Specifically, analysing an ordinal outcome with e.g. ordinal logistic regression regression is more efficient (be it at the price of an assumption, "proportional odds"). But your audience may more easily understand what the patterns in your data are if you dichotomize the outcome. So, if sample size is large, and effects strong, then it may be easier to dichotomize the outcome at some meaningful cut-off for easy communication of your findings.

2. Nominal/ ordinal/ linear modeling of independent variables (predictors). I suppose there are again several reasonable choices. If you suspect an ordinal relation between a predictor and outcome (either ordinal or dichotomized) I would suggest to start with a linear coding. This is a simple starting point; quite good statistical power (efficient), as long as the relation is monotone. Then you may want to check on whether linearity is reasonable. Harrell (Springer, 2001) and I (Steyerberg, Springer 2009) suggest in our books to go first for a simple extension, i.e. add a square term (x+x^2). With many categories (13 in you example), you may consider more complex transformations as well. Coding as nominal would probably require some regrouping (collapsing of categories). Especially at the tails I suspect you may want to combine say category 1-3 and 11-13? Intermediate categories perhaps per 2 or so? If sample size is large, an analysis as a nominal variable might work fine. Many epidemiologists categorize in 4 or 5 groups. This is statistically inefficient for an ordinal predictor variable, but it is easy to understand what is happening in your data.

3. Related predictors. As remarked by others above, stability of estimated regression coefficients, and hence interpretability, may be a problem. But this problem only arises if we have truly collinear predictors in my experience; you may check the correlation, and if Pearson's r < 0.5 I would not worry. You may also consider the variance inflation factor, with high values pointing at instability.

@ Vignal: where did you get the idea that for a probit model, residuals should be normal? They can't, since the outcome is a Bernoulli variable (in the simple binary case). Eventually, you can say that the latent variable leading to the binary outcome should be normal; but you can also simply say that probit  (or logit, or any other usual) transformation is simply a mathematical tool to convert a [0-1] value (probability) into a real-valued value, on which linear model is meaningful, And then, the only two assumptions are that 1) binary outcomes are independant and 2) in the transformed space, a the relationship between transformed probability and predicors is indeed linear.

@ Ann: you may try a numeric coding of your levels and plot them against your predictors, then do a loess curve on that and compare the result to a sigmoid curve [logit model], or to the normal cumulative distribution function [probit model]. Not so easy anyway. You may try search for "cumulative log-log link", which is an example of asymetrical model, and see how it is detected; I am not a specialist about that, sorry...

@ Ewout; for point 3, another difficulty with colinearity is that order of variables in the model may change their p-values (but not their coefficients) for some test methods, so choice of the test must be done with great care. This can happen even with small colinearity.

Yes ordinal regression is appropriate to relate voting choice to the two predictors.  This is equivalent to fitting a Generalized Linear Model assuming a Multinomial distribution and a Cumulative Logit link function.

Yes, collinearity is a problem in model fitting because it causes the parameter estimates to become unstable.  Check the strength of the relationship between the two predictors using Pearson correlation.  If it is less than 0.5 you shouldn't worry about collinearity.

It is an understandable point that residuals refer to the differences between real values of outcome and predicted values of outcome(that are tied up with the combinations of predictors(mixture of continuous and categorical variables), and not just outcome, Dr. Emmanuel. It is a known fact that polychotomous/dichotomous mode of dependent variable is not normally distributed and I do not deny that. But, when it comes to predictors, if the combinational effects of predictors are normally distributed, then, it is better to deal with binomial/multinomial mode of probit regression otherwise, it relates to binomial/multinomial mode of logit regression. Yes, it is true that differences between the  probability mode(predictand/outcome) and predictor should be following the normal mode of distribution and you may need to deal with probit model if that is the case. I have pointed out the statement in an indirect way. I do have justifications and evidences to indicate the validity of my statements. Thank you.

@Vignes: what you describe seems like a latent variable model, and I agree that if the latent variable is Gaussian, probit is more « natural ». But I see not mathematical or statistical reason that forbides to use a logit or probit model for any binary outcome, whatever the latent variable (if any... I don't think that for outcomes like sex, it make sense) is. As far as I know, these are special cases of GLM with different link functions, and there is no normality assumption in such models. If you have some justification and evidences against that, I would be happy to read them.

Another reading of your message suggests that you may think about random effects or mixed effects models. If this is so, I completely agree with you, normal distribution of random effects is one of the usual assumptions. But in the question asked here, given predictors instead looked liked fixed effects.

Best regards,

Thanks for all your help. I will let the info sink in and do some research, since not everything mentioned here is covered in my studies... 

I was also thinking about maybe looking at precarity through an interaction effect. To first look at the link of income and job insecurity seperatly and then to look at the effect job insecurity has on the relationship between income and voting choice/political participation.  So that for example people with higher income are less influenced by job insecurity because they for example have more wealth. Or maybe more influenced because they have more wealth and are afraid to loose what they have. 

I check correlation.

If I look at precarity (income+jobsecurity) with status inconsistenty1(education+profession) the pearson correlation is -.004

If I look at precarity with status inconsistency2(measured as education+income) , the pearson correlation is significant at the 0.01 level at -.168

Ann, your interaction idea has nice explanatory context.  The results could really add to our understanding of how those two constructs act on political behavior.  I would be very interested in reading that study.

Hey Julia, I can send you the results if you like. It is written in Dutch but I will translate them to English. 

Ann,

I just read your question; I will not discuss what the theory background to make choice is. Just discuss how to handle it in practice.

For the factor of scale from1-13, in general you may treat them as continuous variable,

If set it as category, there will be 12 parameters to be estimated. If your sample size is not large, it will cause some problem in the model fitting, such as no-convergence, large standard errors, …

However you may do the cross contingency table analyses for dependent variable X Scale to see the homogeneity dependency; if you can combine some scales; the linearity;

If you can combine some scale group, you may use combined scale as category factor.

If independent is rejected, but not show linear, you may re-assign score.

For the contingency table count, if there are several or more zero counts; treat scale as category is not proper.  

The contingency table analysis should be also done for dependent X 'status inconsistency',

If there are too many zeroes, you need do the data manipulation by combine dependent factor or 'status inconsistency'

For 'status inconsistency', treat it as ordinal category is fine and recommended, it increase the feting power than treat it as nominal,

However you may sign different scores, such as  “1, 1.5, 3.5 4”, or “1,2,3,5”, etc. depending on the difference of the log logit function among the four groups.

Interaction between scale and 'status inconsistency' could be added, when you treat scale as continuous.

Because the dependent variable has 5 levels, the model fitting would be complex and not easy to explain. If you don’t feel confident, you may pick up some level, say extreme left with extreme right, as the subset, to perform the binary logistic modelling. However , the estimates would be not the same as the overall modeling.

Hi, following your questions and answers; I have another question.

If the proportional odds assumption of the ordinal logistic regression is not fulfilled; what should I do?

Thank you.

You may re-assign the score, in fact you can use different scores and than check the Deviance, the smaller the better.