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I am trying to do a factor analysis with 3 variables (11 point response scale) and 220 cases but am getting an error message and no idea why:
The number of degrees of freedom (0) is not positive. Factor analysis may not be appropriate. Can anyone help me figure out why? ps I get a similar message when i try to do it in MPlus 
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You would do much better to post your syntax.
Degrees of freedom are NOT typically relevant in most applications of EFA in SPSS. Are you perhaps using AMOS and mispecifying your model? If so then review some basic texts about minimal requirements for model identification.
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In reply to this post by CC
Are there missing data?
What are your 3 variables? What are 3 correlation coefficients? 1 vs 2, 1 vs 3, 2 vs 3? What is your syntax? What is the purpose of the factor analysis? If you do a 3D scatterplot, does anything look oddball? Do your 2 variables add up to a constant?
Art Kendall
Social Research Consultants 
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In reply to this post by David Marso
Thanks for your response. I'm using SPSS rather than amos.
This is the syntax: DATASET ACTIVATE DataSet1. FACTOR /VARIABLES Dg4 Dg5 Dg6 /MISSING LISTWISE /ANALYSIS Dg4 Dg5 Dg6 /PRINT INITIAL KMO EXTRACTION ROTATION /FORMAT SORT /PLOT EIGEN /CRITERIA MINEIGEN(1) ITERATE(25) /EXTRACTION ML /CRITERIA ITERATE(25) DELTA(0) /ROTATION OBLIMIN. 
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In reply to this post by Art Kendall
Hi
Thanks for your response. The three variables are attitude questions. I am trying to see if they load onto the same factor in order to establish if I can sum them to form an attitude scales. There are some missing data but not very much. These are the correlations between the variables: Correlations Dg4 Dg5 Dg6 Dg4 Pearson Correlation 1 .578** .719** Sig. (2tailed) .000 .000 N 220 220 220 Dg5 Pearson Correlation .578** 1 .720** Sig. (2tailed) .000 .000 N 220 220 220 Dg6 Pearson Correlation .719** .720** 1 Sig. (2tailed) .000 .000 N 220 220 220 ** Correlation is significant at the 0.01 level (2tailed). Thanks 
Do you have different sets of items that are intended to measure different constructs?
I.e., these three items are intended to measure one attitude construct and there are other set of items meant to measure others? If that is so why not put all of the items for all of the constructs into one analysis? if you are constructing scales why would you not use varimax rotation? If there is only one attitude construct, I suggest you use RELIABILITY to look at the internal consistency. When you do the 3D scatterplot what do you see?
Art Kendall
Social Research Consultants 
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In reply to this post by CC
While the formula for df is not spelled out in the algorithms document I suspect it is something along the lines of p*(p1)/2k where p is the number of variables, k is the number of estimated parameters (loadings). That would yield 0 df with a 3 variable analysis. Inspection of 3, 4, and 5 variable simulations bears out my conjecture.
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In reply to this post by Art Kendall
Thanks for your response
I have done reliability analysis. Alpha reliability is .86. Yes there are other items to measure other constructs but I'm building up the model gradually. I'm not using varimax because i don't expect all factors to be orthogonal I haven't done a plot  to be honest I wouldn't know what to look for. Have you any idea why this message is coming up? 
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In reply to this post by David Marso
Thanks for your comment David.
Can you explain what you mean?  Im not sure I follow what you are saying? And what do you suggest i need to do to get the factor analysis to run? 
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There is really nothing to explain that isn't clearly specified in my comment.
Basically 33=0! Why are you using Maximum Likelihood extraction in the first place? If you insist on using ML with only 3 variables you will get precisely this error/warning message. Perhaps curl up with a decent book on factor analysis before pressing onward. 
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Perhaps but I am an spss user rather than a statistician so don't really follow what you mean
Plus i have done factor analyses with only 3 variables before (expecting a single factor solution) and it worked fine so I am wondering why it would be different in this instance? 
In reply to this post by David Marso
Unless you have an unusually advanced knowledge of factor analysis, for scale construction I suggest that you use the traditional principal axes extraction and varimax rotation.
Principal axes because you would only be interested in the common variance across the items. Varimax rotation because you want your final measures to have divergent validity from each other. How many attitude constructs do you have in your data? How did you decide to have only 3 items to measure a construct? Have these items been used to measure these constructs in previous research? How many items are there combined for all of the constructs? What is your listwise N across all of the items?
Art Kendall
Social Research Consultants 
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In reply to this post by CC
If you told us the means and SDs for your 3 variables too, folks who are interested could attempt to duplicate the problem, and then play around with the model if they were so inclined. In the following MATRIX DATA syntax, replace M1M3 and SD1SD3 with your means and SDs.
MATRIX DATA VARIABLES=ROWTYPE_ Dg4 Dg5 Dg6. BEGIN DATA MEAN M1 M2 M3 STDDEV SD1 SD2 SD3 N 220 220 220 CORR 1 CORR .578 1 CORR .719 .720 1 END DATA. FACTOR MATRIX IN(COR=*) /ANALYSIS Dg4 Dg5 Dg6 /PRINT INITIAL KMO EXTRACTION ROTATION /FORMAT SORT /PLOT EIGEN /CRITERIA MINEIGEN(1) ITERATE(25) /EXTRACTION ML /CRITERIA ITERATE(25) DELTA(0) /ROTATION OBLIMIN /METHOD=CORRELATION. HTH.

Bruce Weaver bweaver@lakeheadu.ca http://sites.google.com/a/lakeheadu.ca/bweaver/ "When all else fails, RTFM." NOTE: My Hotmail account is not monitored regularly. To send me an email, please use the address shown above. 
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In reply to this post by CC
I am suggesting that you are in a position similar to homeowner, unfamiliar with the function of a pipewrench opting to do their own plumbing.
Familiarize yourself with your tools! Look up the term degrees of freedom for a start. Fundamentally, this really has NOTHING to do with SPSS per se. ANY correct software doing ML extraction (with no additional constraints such as setting the 3 loadings equal ) with 3 variables will yield 0 df. You have 3 correlation coefficients. You are estimating 3 factor loadings. The difference between these are the number of degrees of freedom. In this case 0! Real Stats Real Easy ARGH! I always hated that slogan.
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In reply to this post by Bruce Weaver
Bruce,
Please read my explanation of the problem. ML extraction with 3 variables and no additional constraints will yield 0 df. David
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Breaking it down to basic essentials:
MATRIX DATA VARIABLES=ROWTYPE_ Dg4 Dg5 Dg6 Dg7 Dg8. BEGIN DATA MEAN 0 0 0 0 0 STDDEV 1 1 1 1 1 N 220 220 220 220 220 CORR 1 CORR .5 1 CORR .5 .5 1 CORR .5 .5 .5 1 CORR .5 .5 .5 .5 1 END DATA. /* df=0 =3*(31)/2  3 */. FACTOR MATRIX IN(COR=*) /ANALYSIS Dg4 Dg5 Dg6 /EXTRACTION ML . /* df=2 =4*(41)/2  4 */. FACTOR MATRIX IN(COR=*) /ANALYSIS Dg4 Dg5 Dg6 Dg7 /EXTRACTION ML . /* df=5 =5*(51)/2 5 */. FACTOR MATRIX IN(COR=*) /ANALYSIS Dg4 Dg5 Dg6 Dg7 Dg8 /EXTRACTION ML .
Please reply to the list and not to my personal email.
Those desiring my consulting or training services please feel free to email me.  "Nolite dare sanctum canibus neque mittatis margaritas vestras ante porcos ne forte conculcent eas pedibus suis." Cum es damnatorum possederunt porcos iens ut salire off sanguinum cliff in abyssum?" 
In reply to this post by David Marso
Given the stated goal, it may make more sense to use something like coefficient alpha (reliability) that either PCA or FA as a way of determining whether or not adding the scores is justifiable.
Harley Dr. Harley Baker Professor of Psychology California State University Channel Islands Sent from my iPad > On May 18, 2017, at 3:16 PM, David Marso <[hidden email]> wrote: > > Bruce, > Please read my explanation of the problem. > ML extraction with 3 variables and no additional constraints will yield 0 > df. > David > > > Bruce Weaver wrote >> If you told us the means and SDs for your 3 variables too, folks who are >> interested could attempt to duplicate the problem, and then play around >> with the model if they were so inclined. In the following MATRIX DATA >> syntax, replace M1M3 and SD1SD3 with your means and SDs. >> >> MATRIX DATA VARIABLES=ROWTYPE_ Dg4 Dg5 Dg6. >> BEGIN DATA >> MEAN M1 M2 M3 >> STDDEV SD1 SD2 SD3 >> N 220 220 220 >> CORR 1 >> CORR .578 1 >> CORR .719 .720 1 >> END DATA. >> >> FACTOR MATRIX IN(COR=*) >> /ANALYSIS Dg4 Dg5 Dg6 >> /PRINT INITIAL KMO EXTRACTION ROTATION >> /FORMAT SORT >> /PLOT EIGEN >> /CRITERIA MINEIGEN(1) ITERATE(25) >> /EXTRACTION ML >> /CRITERIA ITERATE(25) DELTA(0) >> /ROTATION OBLIMIN >> /METHOD=CORRELATION. >> >> >> HTH. >> CC wrote >>> Hi >>> Thanks for your response. >>> The three variables are attitude questions. I am trying to see if they >>> load onto the same factor in order to establish if I can sum them to form >>> an attitude scales. >>> There are some missing data but not very much. >>> >>> These are the correlations between the variables: >>> >>> Correlations >>> Dg4 Dg5 Dg6 >>> Dg4 Pearson Correlation 1 .578** .719** >>> Sig. (2tailed) .000 .000 >>> N 220 220 220 >>> Dg5 Pearson Correlation .578** 1 .720** >>> Sig. (2tailed) .000 .000 >>> N 220 220 220 >>> Dg6 Pearson Correlation .719** .720** 1 >>> Sig. (2tailed) .000 .000 >>> N 220 220 220 >>> ** Correlation is significant at the 0.01 level (2tailed). >>> >>> >>> >>> Thanks > > > > > >  > Please reply to the list and not to my personal email. > Those desiring my consulting or training services please feel free to email me. >  > "Nolite dare sanctum canibus neque mittatis margaritas vestras ante porcos ne forte conculcent eas pedibus suis." > Cum es damnatorum possederunt porcos iens ut salire off sanguinum cliff in abyssum?" >  > View this message in context: http://spssxdiscussion.1045642.n5.nabble.com/Thenumberofdegreesoffreedom0isnotpositiveFactoranalysismaynotbeappropriatetp5734180p5734199.html > Sent from the SPSSX Discussion mailing list archive at Nabble.com. > > ===================== > To manage your subscription to SPSSXL, send a message to > [hidden email] (not to SPSSXL), with no body text except the > command. To leave the list, send the command > SIGNOFF SPSSXL > For a list of commands to manage subscriptions, send the command > INFO REFCARD ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD 
In reply to this post by David Marso
Just a couple of points:
(1) If I am not mistaken, the general formula for degrees of freedom in factor analysis is df= [(p  k}^2  (p + k)]/2 where p = number of empirical variable and k = number of factors. (see http://tinyurl.com/googleFAdf ) If one has 3 empirical variables and assumes that there is only one general factor, then df= [(3  1)^2  (3 + 1)]/2 = [(2)^2  5]/2 = [4  4]/2 df = 0/2 = 0 A situation with df=0 means that that the model (here, a single factor) is "just identified". You can get a solution but it is not unique. That is, the loading of variables on the factors, the variances and covariances, are not uniquely determined. A confirmatory factor analysis would require you to set constraints on these (e.g., all loadings are equal, etc.). But this would not explain why you got an error message saying that you have negative degrees of freedom. (2) I'm inferring from your syntax (provided below), that SPSS extracted 2 factors. If it did then the df df= [(3 2)^2  (3 + 2)]/2 = [1  5]/2 = 2 The OP's use of mineigen(1) means that all factors with eigenvalue greater than 1 will used and the presence of a ROTATION command implies that at least 2 factors are present  one doesn't rotate a single factor. If the OP doesn't want to do a CFA, let me suggest the following substitutions: /criteria=factors(1) (extract only one factor) and /rotation norotate. (don't even think of rotating the solution) SPSS' factor doesn't do confirmatory factor analysis but you can determine how well certain models fit but only in a very limited way. AMOS will do CFA but one has to really know what their measurement model is. The OP should take a look at the following article, not because it provide you a solution to his situation but as a starting point to the issues he will have to deal with: http://journals.sagepub.com/doi/abs/10.1177/0013164412457367?journalCode=epma Mike Palij New York University [hidden email] > DATASET ACTIVATE DataSet1. > FACTOR > /VARIABLES Dg4 Dg5 Dg6 > /MISSING LISTWISE > /ANALYSIS Dg4 Dg5 Dg6 > /PRINT INITIAL KMO EXTRACTION ROTATION > /FORMAT SORT > /PLOT EIGEN > /CRITERIA MINEIGEN(1) ITERATE(25) > /EXTRACTION ML > /CRITERIA ITERATE(25) DELTA(0) > /ROTATION OBLIMIN.  Original Message  On Thursday, May 18, 2017 5:30 PM, David Marso wrote; > There is really nothing to explain that isn't clearly specified in my > comment. > Basically 33=0! > Why are you using Maximum Likelihood extraction in the first place? > If you insist on using ML with only variables you will get precisely > this > error/warning message. > Perhaps curl up with a decent book on factor analysis before pressing > onward. >  > > CC wrote >> Thanks for your comment David. >> Can you explain what you mean?  Im not sure I follow what you are >> saying? >> And what do you suggest i need to do to get the factor analysis to >> run? ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD 
In reply to this post by Baker, Harley
The recent psychometric literature is not positive on alpha,
especially when the assumptions are not met. One source to read before calculating alpha is the following: Dunn, T. J., Baguley, T., & Brunsden, V. (2014). From alpha to omega: A practical solution to the pervasive problem of internal consistency estimation. British Journal of Psychology, 105(3), 399412. And these authors are nice about it. Mike Palij New York University [hidden email]  Original Message  On Thursday, May 18, 2017 7:29 PM, Baker, Harley wrote: Given the stated goal, it may make more sense to use something like coefficient alpha (reliability) that either PCA or FA as a way of determining whether or not adding the scores is justifiable. Harley Dr. Harley Baker Professor of Psychology California State University Channel Islands Sent from my iPad > On May 18, 2017, at 3:16 PM, David Marso <[hidden email]> > wrote: > > Bruce, > Please read my explanation of the problem. > ML extraction with 3 variables and no additional constraints will > yield 0 > df. > David > > > Bruce Weaver wrote >> If you told us the means and SDs for your 3 variables too, folks who >> are >> interested could attempt to duplicate the problem, and then play >> around >> with the model if they were so inclined. In the following MATRIX >> DATA >> syntax, replace M1M3 and SD1SD3 with your means and SDs. >> >> MATRIX DATA VARIABLES=ROWTYPE_ Dg4 Dg5 Dg6. >> BEGIN DATA >> MEAN M1 M2 M3 >> STDDEV SD1 SD2 SD3 >> N 220 220 220 >> CORR 1 >> CORR .578 1 >> CORR .719 .720 1 >> END DATA. >> >> FACTOR MATRIX IN(COR=*) >> /ANALYSIS Dg4 Dg5 Dg6 >> /PRINT INITIAL KMO EXTRACTION ROTATION >> /FORMAT SORT >> /PLOT EIGEN >> /CRITERIA MINEIGEN(1) ITERATE(25) >> /EXTRACTION ML >> /CRITERIA ITERATE(25) DELTA(0) >> /ROTATION OBLIMIN >> /METHOD=CORRELATION. >> >> >> HTH. >> CC wrote >>> Hi >>> Thanks for your response. >>> The three variables are attitude questions. I am trying to see if >>> they >>> load onto the same factor in order to establish if I can sum them to >>> form >>> an attitude scales. >>> There are some missing data but not very much. >>> >>> These are the correlations between the variables: >>> >>> Correlations >>> Dg4 Dg5 Dg6 >>> Dg4 Pearson Correlation 1 .578** .719** >>> Sig. (2tailed) .000 .000 >>> N 220 220 220 >>> Dg5 Pearson Correlation .578** 1 .720** >>> Sig. (2tailed) .000 .000 >>> N 220 220 220 >>> Dg6 Pearson Correlation .719** .720** 1 >>> Sig. (2tailed) .000 .000 >>> N 220 220 220 >>> ** Correlation is significant at the 0.01 level (2tailed). >>> >>> >>> >>> Thanks > > > > > >  > Please reply to the list and not to my personal email. > Those desiring my consulting or training services please feel free to > email me. >  > "Nolite dare sanctum canibus neque mittatis margaritas vestras ante > porcos ne forte conculcent eas pedibus suis." > Cum es damnatorum possederunt porcos iens ut salire off sanguinum > cliff in abyssum?" >  > View this message in context: > http://spssxdiscussion.1045642.n5.nabble.com/Thenumberofdegreesoffreedom0isnotpositiveFactoranalysismaynotbeappropriatetp5734180p5734199.html > Sent from the SPSSX Discussion mailing list archive at Nabble.com. > > ===================== > To manage your subscription to SPSSXL, send a message to > [hidden email] (not to SPSSXL), with no body text except > the > command. To leave the list, send the command > SIGNOFF SPSSXL > For a list of commands to manage subscriptions, send the command > INFO REFCARD ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD 
I know, alpha, is not an ideal measure. But, if it works as it is supposed to, it can give some valuable information concerning the degree to which the common sources of variance can be combined together into an index. My concern in this case is that there are three variables to be summed into one scale. (Threeitem scales are not ideal.) We do not know the metric (7pt Likert, 5pt Likert, binary or something else?) something that is important to know when trying to combine items together. These would be important to know . . . and without knowing the degree to which the data conform to alpha assumptions, it would not be optimal to simply use that approach. (In general, my preference, if the assumptions are met, would be to explore IRT possibilities.)
harley Dr. Harley Baker Professor of Psychology Madera Hall 2413 California State University Channel Islands One University Drive Camarillo, CA 93012 805.437.8997 (p) 805.437.8951 (f) [hidden email] ________________________________________ From: SPSSX(r) Discussion <[hidden email]> on behalf of Mike Palij <[hidden email]> Sent: Thursday, May 18, 2017 7:05 PM To: [hidden email] Subject: Re: The number of degrees of freedom (0) is not positive. Factor analysis may not be appropriate. The recent psychometric literature is not positive on alpha, especially when the assumptions are not met. One source to read before calculating alpha is the following: Dunn, T. J., Baguley, T., & Brunsden, V. (2014). From alpha to omega: A practical solution to the pervasive problem of internal consistency estimation. British Journal of Psychology, 105(3), 399412. And these authors are nice about it. Mike Palij New York University [hidden email]  Original Message  On Thursday, May 18, 2017 7:29 PM, Baker, Harley wrote: Given the stated goal, it may make more sense to use something like coefficient alpha (reliability) that either PCA or FA as a way of determining whether or not adding the scores is justifiable. Harley Dr. Harley Baker Professor of Psychology California State University Channel Islands Sent from my iPad > On May 18, 2017, at 3:16 PM, David Marso <[hidden email]> > wrote: > > Bruce, > Please read my explanation of the problem. > ML extraction with 3 variables and no additional constraints will > yield 0 > df. > David > > > Bruce Weaver wrote >> If you told us the means and SDs for your 3 variables too, folks who >> are >> interested could attempt to duplicate the problem, and then play >> around >> with the model if they were so inclined. In the following MATRIX >> DATA >> syntax, replace M1M3 and SD1SD3 with your means and SDs. >> >> MATRIX DATA VARIABLES=ROWTYPE_ Dg4 Dg5 Dg6. >> BEGIN DATA >> MEAN M1 M2 M3 >> STDDEV SD1 SD2 SD3 >> N 220 220 220 >> CORR 1 >> CORR .578 1 >> CORR .719 .720 1 >> END DATA. >> >> FACTOR MATRIX IN(COR=*) >> /ANALYSIS Dg4 Dg5 Dg6 >> /PRINT INITIAL KMO EXTRACTION ROTATION >> /FORMAT SORT >> /PLOT EIGEN >> /CRITERIA MINEIGEN(1) ITERATE(25) >> /EXTRACTION ML >> /CRITERIA ITERATE(25) DELTA(0) >> /ROTATION OBLIMIN >> /METHOD=CORRELATION. >> >> >> HTH. >> CC wrote >>> Hi >>> Thanks for your response. >>> The three variables are attitude questions. I am trying to see if >>> they >>> load onto the same factor in order to establish if I can sum them to >>> form >>> an attitude scales. >>> There are some missing data but not very much. >>> >>> These are the correlations between the variables: >>> >>> Correlations >>> Dg4 Dg5 Dg6 >>> Dg4 Pearson Correlation 1 .578** .719** >>> Sig. (2tailed) .000 .000 >>> N 220 220 220 >>> Dg5 Pearson Correlation .578** 1 .720** >>> Sig. (2tailed) .000 .000 >>> N 220 220 220 >>> Dg6 Pearson Correlation .719** .720** 1 >>> Sig. (2tailed) .000 .000 >>> N 220 220 220 >>> ** Correlation is significant at the 0.01 level (2tailed). >>> >>> >>> >>> Thanks > > > > > >  > Please reply to the list and not to my personal email. > Those desiring my consulting or training services please feel free to > email me. >  > "Nolite dare sanctum canibus neque mittatis margaritas vestras ante > porcos ne forte conculcent eas pedibus suis." > Cum es damnatorum possederunt porcos iens ut salire off sanguinum > cliff in abyssum?" >  > View this message in context: > http://spssxdiscussion.1045642.n5.nabble.com/Thenumberofdegreesoffreedom0isnotpositiveFactoranalysismaynotbeappropriatetp5734180p5734199.html > Sent from the SPSSX Discussion mailing list archive at Nabble.com. > > ===================== > To manage your subscription to SPSSXL, send a message to > [hidden email] (not to SPSSXL), with no body text except > the > command. To leave the list, send the command > SIGNOFF SPSSXL > For a list of commands to manage subscriptions, send the command > INFO REFCARD ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD ===================== To manage your subscription to SPSSXL, send a message to [hidden email] (not to SPSSXL), with no body text except the command. To leave the list, send the command SIGNOFF SPSSXL For a list of commands to manage subscriptions, send the command INFO REFCARD 
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