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I have collected data for a PhD thesis, and need help understanding how to build a road map to do analytical and statistical analysis. The PhD is not itself in statistics or machine learning, but I would like to understand what are the steps and type of analysis that I have to follow for analysing data for an advanced degree? In general, how should I approach such a problem?

In the data I have collected, there are 623 observations including one continuous dependent variable and 13 independent variables (continuous, categorical, and ordinal) that are defined based on the researcher experience and literature review.

I considered planning to do several regression analysis to predict the dependent variable and study the effective factors (if they are positive, negative, and their magnitude) on it. I've tried multiple linear regression including different transformation on independent variables. On the other hand, I'm not sure if I should study each independent variables through the time and forecast their values in the time horizon?

Here are the steps in my mind so far:

  1. Plotting the scatter plots of different independent variables vs dependent variable to define outliers and check if the model is linear also with respect to coefficients
  2. Removing the potential outliers
  3. Splitting the data into two data sets to build the model and validate it after that.

    If the model is linear then:

  4. Performing the multiple linear regression

  5. Performing the multiple linear regression including different transformations to enhance the model
  6. Validating the model
  7. Doing the quantile regression
  8. Doing supervised learning machine etc.

If the model is not linear, I may instead need to use non-linear statistical techniques.

Any feedback would be highly appreciated. My goal is to build a clear and robust road map for this part of the work.

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    $\begingroup$ I don't think you've said what you are trying to do. Predict the dependent variable? what regression have you tried? $\endgroup$ – Sean Owen Sep 19 '15 at 7:05
  • $\begingroup$ I explained that I want to predict the dependent variable and study the coefficients also. I mentioned what analysis I have done so far. Thank you. $\endgroup$ – Amir Sep 19 '15 at 21:23
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    $\begingroup$ . . . unless you are asking about analysis for data collected as part of your PhD (which you are studying now)? In which case I think it may be time to talk things through with your advisor. $\endgroup$ – Neil Slater Sep 20 '15 at 8:20
  • $\begingroup$ Thank you Neil. I'm doing the analysis for data collected as part of my PhD. I had some graduate statistical analysis courses but they were not as helpful and structured as I expected. On the other hand, my adviser is not well-experienced in this field. Hence, I want to get the experienced advice to build a clear plan for my analysis which must be heavy enough for PhD also. Here are the different steps in my mind so far: 1- Plotting the scatter plots of different independent variables vs dependent variable to define outliers and check if the model is linear also with respect to coefficients $\endgroup$ – Amir Sep 20 '15 at 12:39
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    $\begingroup$ I would completely avoid removing "potential outliers". You should certainly identify values that seem a bit odd and if there is some clear reason for removing or changing the value (such that from field notes you see that there is a transcription error), only then remove them. But otherwise, that's data which should be kept. Everything else might be just noise. $\endgroup$ – JimB Sep 21 '15 at 21:24
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Typically, quantitative analysis is planned and performed, based on research study's goals. Focusing on research goals and corresponding research questions, researcher would propose a model (or several models) and a set of hypotheses, associated with the model(s). Model(s) and its/their elements' types usually dictate (suggest) quantitative approaches that would make sense in a particular situation. For example, if your model includes latent variables, you would have to use appropriate methods to perform data analysis (i.e., structural equation modeling). Otherwise, you can apply a variety of other methods, such as time series analysis or, as you mentioned, multiple regression and machine learning. For more details on research workflow with latent variables, also see section #3 in my relevant answer.

One last note: whatever methods you use, pay enough attention to the following two very important aspects - performing full-scale exploratory data analysis (EDA) (see my relevant answer) and trying to design and perform your analysis in the reproducible research fashion (see my relevant answer).

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  • $\begingroup$ @ Aleksander, I went through all your reference posts which were really helpful but here are some more questions: 1. Imagine my research goal is to define the significant variables on the dependents variables, what kind of analysis do you advice rather than regression? 2. Do you aware of any regression methods that are more advanced and general (I mean no need all the independent variables follow normal distribution) 3. I’m assuming I have some latent variables? How do you approach that? 4. Would mind telling me what the difference are between machine learning and regression methods? Thanks. $\endgroup$ – Amir Sep 22 '15 at 17:06
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    $\begingroup$ @Amir: I'm glad that my info helped. In regard to your question, unfortunately, it is impossible for me to answer your questions in detail, as each question is quite broad. However, the following are my brief answers. 1. That cannot be your research goal, unless your topic is statistical analysis itself - IMHO, you should formulate research goals in terms of your problem's subject domain. Regardless, your sentence is not clear to me. 2. AFAIK, some multivariate methods do not have data normality assumption (i.e., PLS-SEM). (to be continued) $\endgroup$ – Aleksandr Blekh Sep 22 '15 at 17:25
  • $\begingroup$ @Amir: (cont'd) Speaking about regression per se, read about robust regression methods. Also see this discussion, which reminds that normality assumption applies to residuals, not data itself. 3. Start with Wikipedia. Then try this tutorial and/or these Mplus tutorials. (to be continued) $\endgroup$ – Aleksandr Blekh Sep 22 '15 at 17:48
  • $\begingroup$ @Amir: (cont'd) 4. I would say that the main difference between ML and regression is as follows. Regression is a relatively low-level set of methods to establish relatively simple statistical relationships, whereas ML is a much more sophisticated set of learning from data methods, some of which use regression under the hood. For more reading, see this, this as well as this and links within. Hope that was helpful. $\endgroup$ – Aleksandr Blekh Sep 22 '15 at 17:57
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    $\begingroup$ @ Aleksander, thank you for your very helpful response. In fact, I'm thinking to have the following research goals: 1-Finding the relation and significance level of each independent variables with respect to dependent variable. 2– Obtaining the best possible model that could be able to estimate my independent variable 3- Studying each independent variables over the time and use some forecasting methods to predict them over the time horizon. Please let me know if you have any advice. $\endgroup$ – Amir Sep 23 '15 at 13:17

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