factor scores - explanation?
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factor scores - explanation?
 
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Hello, i spent hours browsing the spss archives and the internet and still cannot grasp what exactly the factor scores represent.
Assuming that I run the syntax below, I get three new variables containing factor scores. Let's look at the first one, FAC1_1 (renamed as coredep). What does each score in this new variable really represent for each individual? Is it calculated based on the relationship between the three observed variables and the first factor? If yes, is is some kind of averaged regression coefficient of those three observed variables predicting the first factor (component)? Or does it only represent the relationship of the observed variable that loads highest on Factor 1 and that Factor? If yes, then is it a standardized regression coefficient of that observed variable predicting the factor? FACTOR /VARIABLES dep1 dep2 dep3 /MISSING LISTWISE /ANALYSIS dep1 dep2 dep3 /PRINT INITIAL EXTRACTION /CRITERIA FACTORS(3) ITERATE(25) /EXTRACTION PC /ROTATION NOROTATE /SAVE REG(ALL) RENAME VARIABLES (FAC1_1 = coredep) VARIABLE LABELS coredep "CORE SCORE: DEPRESSION" ===================== 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 |
Re: factor scores - explanation?
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Bozena:
The factors could be intuitively understood as variables independent one from each other (that is, unless you do an oblique rotation and get correlated factors but that is out of the question now), variables which explain a (possibly large) part of the total variance of the observed variables. The first factor is the one explaining most. As part of the output in SPSS you get the percentage of variance explained by each factor. Since the observed variables are standardized during the procedure, with zero mean and unit STD DEV, their variance is also 1. Therefore for k variables the total variance is 1 x k = k. Part of that variable is explained by the first factor. Now, the factor scores can be interpreted as the scores that your subjects need to have in the underlying factor, if this factor is to explain that amount of variance. As the factor is a mere construct, it is measured on a standardized scale with zero mean and STDDEV=1. Therefore if a particular individual gets a factor score of 2, it means he is two standard deviations above the mean of the factor. If all your variables were tests of cognitive ability, your first factor could be interpreted as a measure of general cognitive ability, and that particular individual would be 2 SD above the mean (which is an IQ of about 115). Actually, IQ scores are based on factor scores generated by a number of separate intelligence tests. Factor scores can be estimated in various ways (the default way is the REGRESSION method, but there are other options). To keep things simple I do not go into those methods of numerical estimation: you can grasp intuitively that there are possibly more than one set of values that accomplish that function as factor scores. As in any regression, these factor scores are obtained as a linear combination of the observed variables, something like: F1i = b1X1+b2X2+...+bkXk. There is no constant in the equation because all variables are standardized z-scores. And there is no error term either, because it is not an "estimation" of a regression but a deterministic function of the observed variables. These "b" coefficients are in the SPSS output as a matrix of component score coefficients. Hope this dispels some of your doubts. Harman, Modern Factor Analysis, a classic in this field, has a nice explanation of this matter. Hector -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Bozena Zdaniuk Sent: 28 December 2009 20:39 To: [hidden email] Subject: factor scores - explanation? Hello, i spent hours browsing the spss archives and the internet and still cannot grasp what exactly the factor scores represent. Assuming that I run the syntax below, I get three new variables containing factor scores. Let's look at the first one, FAC1_1 (renamed as coredep). What does each score in this new variable really represent for each individual? Is it calculated based on the relationship between the three observed variables and the first factor? If yes, is is some kind of averaged regression coefficient of those three observed variables predicting the first factor (component)? Or does it only represent the relationship of the observed variable that loads highest on Factor 1 and that Factor? If yes, then is it a standardized regression coefficient of that observed variable predicting the factor? FACTOR /VARIABLES dep1 dep2 dep3 /MISSING LISTWISE /ANALYSIS dep1 dep2 dep3 /PRINT INITIAL EXTRACTION /CRITERIA FACTORS(3) ITERATE(25) /EXTRACTION PC /ROTATION NOROTATE /SAVE REG(ALL) RENAME VARIABLES (FAC1_1 = coredep) VARIABLE LABELS coredep "CORE SCORE: DEPRESSION" ===================== 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 ===================== 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 |
Re: factor scores - explanation?
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In reply to this post by Zdaniuk, Bozena-3
Sorry, I'm on the road and can't get the exact title but I recall an excellent paper by Bruce Thompson at Texas A&M on just this topic. Do a Google Scholar search and you are likely to find him. I seem to recall I retrieved the article directly from from his website. It may still be there.
Mark ----- Original Message ----- From: Bozena Zdaniuk [[hidden email]] Sent: 12/28/2009 03:39 PM PST To: [hidden email] Subject: factor scores - explanation? Hello, i spent hours browsing the spss archives and the internet and still cannot grasp what exactly the factor scores represent. Assuming that I run the syntax below, I get three new variables containing factor scores. Let's look at the first one, FAC1_1 (renamed as coredep). What does each score in this new variable really represent for each individual? Is it calculated based on the relationship between the three observed variables and the first factor? If yes, is is some kind of averaged regression coefficient of those three observed variables predicting the first factor (component)? Or does it only represent the relationship of the observed variable that loads highest on Factor 1 and that Factor? If yes, then is it a standardized regression coefficient of that observed variable predicting the factor? FACTOR /VARIABLES dep1 dep2 dep3 /MISSING LISTWISE /ANALYSIS dep1 dep2 dep3 /PRINT INITIAL EXTRACTION /CRITERIA FACTORS(3) ITERATE(25) /EXTRACTION PC /ROTATION NOROTATE /SAVE REG(ALL) RENAME VARIABLES (FAC1_1 = coredep) VARIABLE LABELS coredep "CORE SCORE: DEPRESSION" ===================== 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 ===================== 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 |
Re: factor scores - explanation?
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In reply to this post by Zdaniuk, Bozena-3
Bozena
I use "The Essentials of Factor Analysis" by Child (2006) published by Continuum Books. I found it most helpful especially in the "hard bits". Roy Greenhalgh University of Southampton UK Bozena Zdaniuk wrote: > Hello, i spent hours browsing the spss archives and the internet and still cannot grasp what exactly the factor scores represent. > Assuming that I run the syntax below, I get three new variables containing factor scores. Let's look at the first one, FAC1_1 (renamed as coredep). What does each score in this new variable really represent for each individual? Is it calculated based on the relationship between the three observed variables and the first factor? If yes, is is some kind of averaged regression coefficient of those three observed variables predicting the first factor (component)? Or does it only represent the relationship of the observed variable that loads highest on Factor 1 and that Factor? If yes, then is it a standardized regression coefficient of that observed variable predicting the factor? > > > FACTOR > /VARIABLES dep1 dep2 dep3 > /MISSING LISTWISE > /ANALYSIS dep1 dep2 dep3 > /PRINT INITIAL EXTRACTION > /CRITERIA FACTORS(3) ITERATE(25) > /EXTRACTION PC > /ROTATION NOROTATE > /SAVE REG(ALL) > RENAME VARIABLES (FAC1_1 = coredep) > VARIABLE LABELS > coredep "CORE SCORE: DEPRESSION" > > ===================== > 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 > > ===================== 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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In reply to this post by Hector Maletta
Could someone be so wonderful and tell me how to put two numbers together?
I have a variable A with 3 cases with values 3, 26, 968 and var B with values 1, 6, 51 for the same three cases. I want variable C with values 31. 266. 96851. So, basically joining together two numbers to create the third number that has all the digits of var A with appended digits of var B. Thanks so much in advance! Bozena Bozena Zdaniuk, Ph.D. Human Early Learning Partnership (HELP) College for Interdisciplinary Studies UBC - UVic - SFU - UNBC - TRU - UBCO 440 - 2206 East Mall, Vancouver BC V6T 1Z3 Tel: 604-827-5552 / Fax: 604-822-0640 www.earlylearning.ubc.ca ===================== 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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data list list /a b. begin data 3 1 26 6 968 51 end data. string #temp (a16). compute #temp=concat(ltrim(string(a, f16)), ltrim(string(b, f16))). compute c=number(#temp, f16). list. *I used a width of 16 to make sure it would be wide enough for any valid numeric value. The slightly tricky part is trimming the values when concatenating, and since they're numbers you need to use ltrim, not rtrim.
Could someone be so wonderful and tell me how to put two numbers together? I have a variable A with 3 cases with values 3, 26, 968 and var B with values 1, 6, 51 for the same three cases. I want variable C with values 31. 266. 96851. So, basically joining together two numbers to create the third number that has all the digits of var A with appended digits of var B. Thanks so much in advance! Bozena Bozena Zdaniuk, Ph.D. Human Early Learning Partnership (HELP) College for Interdisciplinary Studies UBC - UVic - SFU - UNBC - TRU - UBCO 440 - 2206 East Mall, Vancouver BC V6T 1Z3 Tel: 604-827-5552 / Fax: 604-822-0640 www.earlylearning.ubc.ca ===================== 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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Bozena,
compute C = A * 10 ** (TRUNC ( LG10 (B) )+1) + B . also do the trick .
Best,
vlad On Thu, Jan 7, 2010 at 2:09 PM, Rick Oliver <[hidden email]> wrote:
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