Dear colleague,

I made a rapid view onto the last page of your PDF document.

Unfortunately, the plot of your regression standardized residual plot shows systematical misfits: the difference between the observed and the expected CP seems to be sinusoidal, what indicates that the immanent system function is not in the set of the regression model function.

The scatter plot expresses this problem by showing you a quite linear border of the arranged patterns at the base. Even in the centre of the plot the patterns seem to be arranged in lines.

I guess this is not the answer you wished to read, but asked for:  (-:

Best regards,

Michael

Professor Suranga,

I have reviewed your PDF file and concur with Professor Heinert: Plot PP has a sinuous line is undesirable. Unfortunately, in applied research that happens with some frequency. Although not why throw away data.

In any case I have reviewed your data and have a question that perhaps can explain your data. The XLS file has 730 scores. I guess that is the total of people who have scores on the dependent variable.

However, the regression only has 341 cases (total df in ANOVA = 340). That is, there is a loss of more than half of the cases. I guess that's a problem of missing data. However, surveys the data are not missing at random. Unlike the lost data often have biases. My first question would be: would not it be possible to use some method to recover missing data? A large loss of data can affect results

Now, I have comments that I want to share with you. First, I see that the intercept of the regression is 9.3. However, the scale range is 10 to 50 points. I fear that the independent variables need to be recoded or transformed (eg centering them) to properly interpret its meaning.

Overall, the model has moderate explanatory power (only 17%). This may indicate that it is not easy to explain the abortion attitudes of people.

Finally I have a question: how calculated each subject's score on the dependent variable? I ask this because I see that the first negative is formulated negatively and therefore has a different meaning to the other.

I'm afraid that my writing raises more questions than answers. But I need more information before suggesting possible solutions.

Best regards, R.

Dear All,

Thank you so much for taking time to review the document and for your valuable comments which are really helpful. I would like to share following information which you have asked in your answers,

Kindly see two attachments for clarifications

Warm Regards,

Suranga

Prof. Suranga, you raise me 3 questions. Not to lengthen these writings I will respond in parts. Now let's focus on the missing data, which are a common problem in applied research. Our group has compared different methods for recovering missing data. Unfortunately our work is in Spanish ... We compared seven methods to recover lost data: listwise deletion, replacement by the mean of the scale, by the item mean, mean the subject, the subject corrected mean, multiple regression, and Expectation-Maximization (EM ). They all have advantages and disadvantages but some are better than others.

And now entering the subject. By default, SPSS eliminates the missing data (listwise deletion). Today we know that listwise deletion is the least desirable method to handle missing data. Listwise deletion is the method you have used. For that reason there is so much difference between their sample (N = 730) and data from the regression analysis (N = 340).

The simplest methods are replacement for the average (or mean of the scale, the item or subject). For you it would be a simple and basic possibility.

Suppose you have an item, which we call Q1. Do the following:

                                    0 = There is data in Q1

                                    1 = No data in Q1.

The value of the regression MissQ1 will tell the effect it has on the dependent variable is not answering the question. In your case the group of singles who supposedly have no sex life.

More refined methods are regression and multiple imputation based on iterative procedures. SPSS has a module to retrieve missing data. These methods are better than the methods of the average potential replacement. But of course, they are also more complex. If you can I encourage you to investigate.

Finally I dare to let two readings on the subject.

Willms, J. D., and Smith, T. (2006). A Manual for Conducting Analyses with Data from TIMSS and PISA (Report prepared for the UNESCO nstitute for Statistics). New Brunswick: Canadian Research Institute for Social Policy. Retrieved May 17, 2011 in: http://www.unb.ca/crisp/pdf/Manual_TIMSS_PISA2005_0503.pdf. The first pages of the document are a good initial introduction to the methods of recovering missing data

As you work with SPSS could also be interested in this reading.

Van Ginkel, J. R., and Van der Ark, L.A. (2005). SPSS syntax for missing

value imputation in test and questionnaire data. Applied Psychological Measurement, 29 (2), 152-153.

II will finish. But I want to leave a question related to the second query you make me (ie, the intercept of the scale and significance of their data). I look at the output of-regression analysis and see the following. Men have 0.86 points women in the DV (ie, women are more pro-abortion). I also see that age has a positive and significant effect on the DV: by 0.15 points each year increases the value in the DV....

And now my question: what do they mean 1.18 points in the Ethnicity variable?

And what does 0.99 points Marital status?

Regards, R

Sachira:

Hi, I just read your question and your results:

For the regression analysis,

1.       You should get the missing value back, you said:

“That is because; I didn’t ask some questions (related to sexual life”,  for such factor you may categorize this factor, missing as one group, make non-missing with several groups, you can just one Way ANOVA with the dependent groups, to see the score changes, if showing linear including missing group. You may sign missing group with the suitable value by simulation, say using a normal distribution (mean=given value, random error = average error from other groups). If linear not showing, use categorical variable for this missing factor.

Using mean value to replace the missing value will increase the p-value, may generate bias.

2.       For some variable, such as ethnicity, married status should be treated as categorical factor. You should not treat them as continuous factors; ANOVA results show them treated to be linear. Only one parameter for those factors. You need generate dummy variable for them:

Say three levels : A, B, C, you should generate two factors

    IfA   (if A, =1, other =0) and  ifB (if B =1, other =0)

3.       You need check the correlation among independent factors:  say education and access to information might be correlated.

The following are the general process for linear regression:

The model selection depends on the test hypothesis and data structure. As you mentioned, you outcome dependent variable should be continuous. You do not check the distribution on dependent variable itself. You need check it in the regression process. As many answers mentioned, the residuals are independent and identical normal distributed rather than the outcome itself. You also need check, the collinearrity of independent factors, which should be independent without errors, and the relationship between the outcome and independent factors, which should be linear by assumption. The whole topic is MODEL building and diagnosis problem, there are many way to do it, according your statement I think the following will be easy. Assume the dependent variable is continuous and normal distributed as you stated

1.       Check the type of co factors, if some have a lot of missing value or typo, correct them or let them out. Then for continuous factors, check the person correlation coefficients,  if Pearson correlation near 1 or -1 among any two, one should be gone in multiple regression. For category factors, check independency of any two. if most count appear in the diagonal of the contingence table, one of the two category variables should be gone.

2.       Draw the scatter plots between the continuous outcome and each independent quantitative factor to see the association: if linear trend is shown, the factor is in, if non-linear effect is shown, transformation is needed. If no trend, like random, the independent factor could be out.

3.       Suppose the dependent variable should be independent. If the dependent variable is related to time, check the auto correlation, if autocorrelation exists,  time series modeling say Autoreg might be used.

4.       Do PCA analysis to see if there are still multicolinearity among the independent factors, if some eigen-value is near zero, you may drop one of them, or define a new factor (transformation) .

5.       If the sample size is large enough, say 10 (at least) times higher of the unknown parameter number, you can  do multiple regressions, you may use auto select option, such as forward backward or best, which will select independent factors for you.

6.       Number of parameters: interception: count 1, continuous factor, each counts 1, categorical factor with level of k, count as k-1.

7.       Check outliers by leverage or CooksD or Residual, if exists you may delete them or do both model with and without the outliers.

8.       Check normality of residuals from the multi variable regression,    if violated, do transformation, variance homogeneity exist: transformation on some independent factor, variance homogeneity doesn’t exist: transformation on dependent factor. Those may improve your model fitting.

9.       You may use Akaike’s information criterion or Bayesian information criterion or Mallows’ CP to decide how many factors should be in. Using them is better than comparison of  R2.

10.   Check interaction among the independent factors, the interaction among two quantitative predictors, means there is joint effect; the effect of one factor varies across the level of another factor. If the interaction between an quantitation factor and a category factor, say gender, it means the effect of the quantitative, slope,  is different between males and females.

 Yuanzhang Li

Dear colleagues,

Thank you very much for your valuable answers which directed me to think differently.

@ Prof. Ruben Fernández-Alonso and prof. Yuanzhang Li

I decided to do following changes to the regression model using your feedback. But, Still I have some technical points to clarify. Could you please help?

1) I’ll recover the missing values at least using replacement for the average method as both of you mentioned. However, I want to clarify that, Is it possible to recover missing values of the answers of “never married” respondents for questions like “Number of living Children” / “Number of pregnancies”? I purposely skipped these questions from never married respondents.

2) I’ll categorize my DV (abortion attitudes) in to three categories using inter quartile range (IQR) as follows

Above Q3 = Liberal attitudes towards abortion OR Pro-choice attitudes

Q1 to Q3 = Moderate / Average attitudes towards abortion

Bellow Q1 = Conservative attitudes towards abortion OR pro-life attitudes

What model is the best option? Multinomial Logistic Regression or Ordinal regression?

3) I’ll compute new dummy variables for nominal variables like marital status, ethnicity. So, there will be more factors in the model. However, my practical experience is that SPSS will ignore some factors which are in-significant when we use step-wise, forward or backward methods. So, my question is, is it OK to use only one or few levels of one variable in the final model? Ex:-Only “Muslims” out of all ethnic groups?

Ex:-

Abortion attitudes = f (Age, gender, number of living children, access to information, Muslim)

Is this the case? OR do we have to keep all the ethnic groups in the model irrespective of the level of significance.

Thanks a lot for your kindness.

Warm Regards,

Suchira

Prof. Suranga impute missing values is to establish a procedure to estimate the most plausible value of a data we lack. In your case the question is: What will be the most likely number of children for a single person?

I do not know the statistics of single mothers (or fathers) in Sri Lanka. In Spain I think that would be close to almost all singles have 0 children. This rarely mistaken me: our statistics says we have few unwanted teenage pregnancies. Somehow it's what you thought: you avoid single people answer those questions.

Another thing is that there is covariation between the variables "marital status = single" and "number of children". Anyway is expected: singles have fewer children and fewer pregnancies than married.

You also asked about the best method of imputation of missing data. Your choice depends on the type and size of the lost data. The average replacement method works well in some cases: if the percentage of missing data is small (around 5%) and loss of data is random. If the loss rate exceeds 10% and the loss is not random is better to use maximum likelihood methods including auxiliary variables. All this you can do with SPSS.

You ask what kind of regression is best for categorical variables. And I ask: Why do you want to convert an approximately continuous variable into a categorical variable? You will lose variance in DV. Generally in social studies we are going in the opposite direction: we transform discrete variables into continuous.

In any case, reflect on the criteria you will use to convert discrete variable: it is a statistical criterion, but nothing substantive. Now you have a 40-point scale (DV range: 10 to 50) and you want to make a scale whose range is 3 points based on Q1-Q3 difference.

I insist on your analysis I would not make a DV that is continuous on a categorical variable. But if you want to do I would advise looking for a substantive standard and not a purely statistical criterion. For example, between 10 and 20 points (pro-abortion); between 40 and 50 points (anti-abortion); between 21 and 39 (neutral, undecided) ... If you want to make categories based on a Likert scale care that these categories reflect the choices of the people response.

And on the scale I have reviewed the document "Study on abortion-1.doc". I do not understand why the item 2 has an inverted scale. I think item 1 should be inverted scale: it is the only one negatively worded.

Regards, R

·        1) I’ll recover the missing values at least using replacement for the average method as both of you mentioned. However, I want to clarify that, Is it possible to recover missing values of the answers of “never married” respondents for questions like “Number of living Children” / “Number of pregnancies”? I purposely skipped these questions from never married respondents.

> You do not need to do it.

Considering DV as continuous is good enough. If the residual is not normal, do trasformation

3) I’ll compute new dummy variables for nominal variables like marital status, ethnicity. So, there will be more factors in the model. However, my practical experience is that SPSS will ignore some factors which are in-significant when we use step-wise, forward or backward methods. So, my question is, is it OK to use only one or few levels of one variable in the final model? Ex:-Only “Muslims” out of all ethnic groups?

Ex:-

Abortion attitudes = f (Age, gender, number of living children, access to information, Muslim)

Is this the case? OR do we have to keep all the ethnic groups in the model irrespective of the level of significance.

>>> You only have a few factors; you do not need using forward/backward/stepwise, to choose factors. You can do the model building by yourself, to keep all dummy variables from the same factor in or out together. You may use Akaike information criterion (AIC)=2p-2Log L to select which factors should be in.

When you use category factor, if possible,  try to choose the level with large size as reference group. The number of groups should not be too high. If you find two levels have similar group, you may combine them, if the factor is nominal, or neighbor level in ordinal.

Dear Courageous, 

Thank you very much for all of your valuable comments and feedback. I am trying to finalize the model. I analyzed same data using

01) Linear regression

02) Ordinal and

03) Multiple Linear Regression

However, I prefer to proceed with the linear model to avoid loss of variance of DV. AND it is easy interpret too.

I have attached herewith the results. One last request, could you please comment on this? Is it OK, if I proceed with the first model?

Kindly see the attachment

Many thanks for your kind help

Warm Regards,

Suchira Suranga

Is the table the software output or summarized by you? Need show the original output.

Need show the frequency distribution of the trasformed factors

If no redundant shown, are they continuous factors? Or still dummy.

for dummy variable: Muslims-transformed, which shows high sig difference, how many in each level? If none is too few, you may run the model by it separately (consider interaction. Check the residuals plots separately

Is oveallrscorelanguage continuous or category original? If continuous,. check the correlation of total score personnel and oveallrscorelanguage as continuous factor

. if continuous, how did you categorize oveallrscorelanguage. The size of transformed=1 seems much larger than transformed =0, or the range of DV is much large for transformed =0, need see the dv distribution for categorized oveallrscorelanguageTansformed.

Prof Suranga:

I have reviewed your data. I see you've been able to recover many of them and the percentage of missing data is small. I also see that R2 has risen from 0.16 to 0.26. So the solution is now better than 12 days ago.

Now I want to ask you some questions. When an output of a regression model to point the first question is interpreted as follows: What is the intercept? In your case the question is: What type of person that will predict 19.49 points? We should know the following: the person who has 19.49 points ...

• is Muslim or not?

• How many children live?

• What level of access to information have?

• What is your personal experience?

• N of peopleinHH what?

• What socioeconomic status?

I give you an example: I understand that the variable "Muslim = 0" means "belonging to a different ethnic group to Muslim" and 1 = "Muslim" If this is so, it would be correct to say. 19.49 points predicted for a Non-mulsuman, and 8.7 points for a Muslim predicted less.

Table regression delete the variable "Muslins_trans = 0" and let the predictor "Muslins = 1", the effect should be -8.726. points.

Continuous variables I recommend centering the variables. Thus the intercept mean "people with average score for continuous variables"

a greeting

Dear Courageous,

Greetings from Sri Lanka

Thank you very much for your valuable feedback and recommendations. It is please to hear that I am improving the model. :-)

I don’t know whether I have correctly captured what both of you suggested. However, I try to use original categorical variables instead of developing scales which is difficult to interpret. Ex:- Access to information. I think now it is more meaningful.

Now, the intercept is greater than last time (36.336). The effect of ethnicity “Muslim” also has been decrease compared to other independent variables. Could you please kindly review the model when you have a free time? Please see the attachment.

Thank you very much in advance.

Suranga