how to interpret bootstrap results of multiple regression

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how to interpret bootstrap results of multiple regression

Faiz Rasool
Dear list,

Firstly, thank you so much for   immensely helpful replies about my
question on homoscedasticity assumption in the context of multiple
regression.

I have used the NCV test available in car package for r, and the
Breusch and pagan test to assess the assumption of homoscedasticity.
Both tests are highly significant, chi-square values above 10, at 1
degree of freedom. I have a dependent variable which is a sum of six
likert items. The response scale was from 1 (never) to 5(always). I’ve
multiple independent variables, all have been measured using likert
items, and scores on those items have been summed to form scales. The
sample size is 1250.

I am reading discovering statistics using SPSs by Field and R in
action data analysis and graphics with R.

Both books suggest that when homoscedasticity is violated, the
standard errors may not be correct, and tests of significance may not
be optimum. In such a situation bootstrapping is suggested. I have
performed bootstrap both using SPSS and R.

My question may be the dumbest question ever asked on this list, so
apologies in advance.

How to interpret results of bootstrap in SPSS and how to report those
results. In the output of SPSS, I have two tables for coefficients.
First is the standard table of coefficients that spss provides in
normal regression output, and the second has bootstrap confidence
intervals, and standard errors.

What I’m unable to work out is that firstly,   can I use the T values
in the coefficients table, as there is no T value at least that is
what I can understand, in the bootstrap table. secondly, in spss
output of bootstrap, the model summary, anova, and coefficients
table appear twice.  I assume that the first set of tables is before
bootstrap, and second set of tables are a part of bootstrap
regression. However, the F value, in the anova table, and the adjusted
r-square are completely unchanged. Is this how it should be?

Lastly, I’m  envisaging the regression results table that I’ll
construct, I believe that the   unstandardized  coefficients, standard
errors, will come from the bootstrap  coefficient table, where to take
the T value from?  Standard coefficient table? The coefficients table
also has sig column and the bootstrap results table also has sig
column, which sig values to report?

Again, sorry for such a basic question.

Regards,
Faiz.

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Re: how to interpret bootstrap results of multiple regression

Ware, William B
In my work, I have found the bootstrapping is effective for dealing with non-normality, but not for heteroscedasticity... To deal with that, I think you need to look at the rlm() function in the MASS package or the use of "sandwich estimation" which requires the car and lmtest packages.  All done in R.

wbw
 
William B. Ware, Ph.D.
McMichael Term Professor of Education, 2011-2013
Educational Psychology, Measurement, and Evaluation
CB #3500 - 118 Peabody Hall 
University of North Carolina at Chapel Hill
Chapel Hill, NC     27599-3500
Office: (919)-962-2511
Fax:    (919)-962-1533
Office:  118 Peabody Hall
EMAIL: [hidden email]
Adjunct Professor, School of Social Work
Academy of Distinguished Teaching Scholars at UNC-Chapel Hill

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of faiz rasool
Sent: Tuesday, February 27, 2018 8:20 AM
To: [hidden email]
Subject: how to interpret bootstrap results of multiple regression

Dear list,

Firstly, thank you so much for   immensely helpful replies about my
question on homoscedasticity assumption in the context of multiple regression.

I have used the NCV test available in car package for r, and the Breusch and pagan test to assess the assumption of homoscedasticity.
Both tests are highly significant, chi-square values above 10, at 1 degree of freedom. I have a dependent variable which is a sum of six likert items. The response scale was from 1 (never) to 5(always). I’ve multiple independent variables, all have been measured using likert items, and scores on those items have been summed to form scales. The sample size is 1250.

I am reading discovering statistics using SPSs by Field and R in action data analysis and graphics with R.

Both books suggest that when homoscedasticity is violated, the standard errors may not be correct, and tests of significance may not be optimum. In such a situation bootstrapping is suggested. I have performed bootstrap both using SPSS and R.

My question may be the dumbest question ever asked on this list, so apologies in advance.

How to interpret results of bootstrap in SPSS and how to report those results. In the output of SPSS, I have two tables for coefficients.
First is the standard table of coefficients that spss provides in normal regression output, and the second has bootstrap confidence intervals, and standard errors.

What I’m unable to work out is that firstly,   can I use the T values
in the coefficients table, as there is no T value at least that is what I can understand, in the bootstrap table. secondly, in spss output of bootstrap, the model summary, anova, and coefficients table appear twice.  I assume that the first set of tables is before bootstrap, and second set of tables are a part of bootstrap regression. However, the F value, in the anova table, and the adjusted r-square are completely unchanged. Is this how it should be?

Lastly, I’m  envisaging the regression results table that I’ll
construct, I believe that the   unstandardized  coefficients, standard
errors, will come from the bootstrap  coefficient table, where to take the T value from?  Standard coefficient table? The coefficients table also has sig column and the bootstrap results table also has sig column, which sig values to report?

Again, sorry for such a basic question.

Regards,
Faiz.

=====================
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=====================
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[hidden email] (not to SPSSX-L), with no body text except the
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Re: how to interpret bootstrap results of multiple regression

Jon Peck
I should point out that the GENLIN procedure (Analyze > Generalized Linear Models > Generalized Linear Models) allows you to run a linear model estimating the covariance model robustly and thereby get good standard errors/significance levels.

On Tue, Feb 27, 2018 at 8:27 AM, Ware, William B <[hidden email]> wrote:
In my work, I have found the bootstrapping is effective for dealing with non-normality, but not for heteroscedasticity... To deal with that, I think you need to look at the rlm() function in the MASS package or the use of "sandwich estimation" which requires the car and lmtest packages.  All done in R.

wbw
 
William B. Ware, Ph.D.
McMichael Term Professor of Education, 2011-2013
Educational Psychology, Measurement, and Evaluation
CB #3500 - 118 Peabody Hall 
University of North Carolina at Chapel Hill
Chapel Hill, NC     27599-3500
Office: <a href="tel:%28919%29-962-2511" value="+19199622511">(919)-962-2511
Fax:    <a href="tel:%28919%29-962-1533" value="+19199621533">(919)-962-1533
Office:  118 Peabody Hall
EMAIL: [hidden email]
Adjunct Professor, School of Social Work
Academy of Distinguished Teaching Scholars at UNC-Chapel Hill

-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of faiz rasool
Sent: Tuesday, February 27, 2018 8:20 AM
To: [hidden email]
Subject: how to interpret bootstrap results of multiple regression

Dear list,

Firstly, thank you so much for   immensely helpful replies about my
question on homoscedasticity assumption in the context of multiple regression.

I have used the NCV test available in car package for r, and the Breusch and pagan test to assess the assumption of homoscedasticity.
Both tests are highly significant, chi-square values above 10, at 1 degree of freedom. I have a dependent variable which is a sum of six likert items. The response scale was from 1 (never) to 5(always). I’ve multiple independent variables, all have been measured using likert items, and scores on those items have been summed to form scales. The sample size is 1250.

I am reading discovering statistics using SPSs by Field and R in action data analysis and graphics with R.

Both books suggest that when homoscedasticity is violated, the standard errors may not be correct, and tests of significance may not be optimum. In such a situation bootstrapping is suggested. I have performed bootstrap both using SPSS and R.

My question may be the dumbest question ever asked on this list, so apologies in advance.

How to interpret results of bootstrap in SPSS and how to report those results. In the output of SPSS, I have two tables for coefficients.
First is the standard table of coefficients that spss provides in normal regression output, and the second has bootstrap confidence intervals, and standard errors.

What I’m unable to work out is that firstly,   can I use the T values
in the coefficients table, as there is no T value at least that is what I can understand, in the bootstrap table. secondly, in spss output of bootstrap, the model summary, anova, and coefficients table appear twice.  I assume that the first set of tables is before bootstrap, and second set of tables are a part of bootstrap regression. However, the F value, in the anova table, and the adjusted r-square are completely unchanged. Is this how it should be?

Lastly, I’m  envisaging the regression results table that I’ll
construct, I believe that the   unstandardized  coefficients, standard
errors, will come from the bootstrap  coefficient table, where to take the T value from?  Standard coefficient table? The coefficients table also has sig column and the bootstrap results table also has sig column, which sig values to report?

Again, sorry for such a basic question.

Regards,
Faiz.

=====================
To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD

=====================
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[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
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--
Jon K Peck
[hidden email]

===================== To manage your subscription to SPSSX-L, send a message to [hidden email] (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD