PCA factor score uses?
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I'm not entirely familiar with PCA and could use some help.
I've used PCA w/varimax rotation to reduce 10 variables (answers to a racism attitudes questionnaire) down to 2 factors. I want to know if the calculated factor scores for each participant can then be used as a dependent variable in subsequent analyses, or whether I should simply combine the variables loading on the respective factors and use those? My problem is in interpreting the factor scores: Group 1 has a mean of -2.72 and Group 2 has a mean of 2.68. These are significantly different, but I'm not sure what the means represent (the raw data are scores ranging from 1 to 10, so there are no negatives). Thanks for any insight. Fred Rose |
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Factor scores are standardized variables, with mean=zero and SD=1,
so it is normal that one group is below 0 and the other is above. One group is high in whatever the factor represents (racist attitudes?), the other is low. If factors are orthogonal, i.e. independent of each other, they represent different, uncorrelated underlying traits your observables variables were measuring. If rotated obliquely they may show certain correlation among themselves. You may treat the scores as dependent variables. You may also interpret them according to the particular variables associated with each factor (i.e. having high loadings on each factor). Hector -----Mensaje original----- De: SPSSX(r) Discussion [mailto:[hidden email]] En nombre de Fredric E. Rose Enviado el: 15 November 2006 04:18 Para: [hidden email] Asunto: PCA factor score uses? I'm not entirely familiar with PCA and could use some help. I've used PCA w/varimax rotation to reduce 10 variables (answers to a racism attitudes questionnaire) down to 2 factors. I want to know if the calculated factor scores for each participant can then be used as a dependent variable in subsequent analyses, or whether I should simply combine the variables loading on the respective factors and use those? My problem is in interpreting the factor scores: Group 1 has a mean of -2.72 and Group 2 has a mean of 2.68. These are significantly different, but I'm not sure what the means represent (the raw data are scores ranging from 1 to 10, so there are no negatives). Thanks for any insight. Fred Rose |
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In reply to this post by Rose, Fred
Fred,
Yes, the scores can be used as dependent variables. Factor scores are standardized with Mean = 0 and SD = 1 , so your groups are quite different from one another. Best, Stephen Brand For personalized and professional consultation in statistics and research design, visit www.statisticsdoc.com -----Original Message----- From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of Fredric E. Rose Sent: Tuesday, November 14, 2006 10:18 PM To: [hidden email] Subject: PCA factor score uses? I'm not entirely familiar with PCA and could use some help. I've used PCA w/varimax rotation to reduce 10 variables (answers to a racism attitudes questionnaire) down to 2 factors. I want to know if the calculated factor scores for each participant can then be used as a dependent variable in subsequent analyses, or whether I should simply combine the variables loading on the respective factors and use those? My problem is in interpreting the factor scores: Group 1 has a mean of -2.72 and Group 2 has a mean of 2.68. These are significantly different, but I'm not sure what the means represent (the raw data are scores ranging from 1 to 10, so there are no negatives). Thanks for any insight. Fred Rose |
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In reply to this post by Rose, Fred
You can use the factor scores in any design role.
Think of the factor scores as z-scores. Mean of zero, SD of 1. What interpretation did you give to the two factors? Are the factors bipolar or unipolar? If you have 2 groups of respondents, and the mean factor scores you mention are for these groups, then group 1 is at one end of the scale and group 2 is at the other. The direction of factors is completely arbitrary. When developing scales, it is traditional to calculate scale scores by summing items, reflecting those items that have negative weights. Since reliability, correlations etc. are not changed by dividing by a constant, you might want to work with a mean of the items. It is also possible that you would want to reflect one or both scales so that the high end is meaningful, e.g., high scores mean more racism. The choice of direction is usually made to make correlations, etc., with other variables have less complex verbal explanations. Art Kendall Social Research Consultants Fredric E. Rose wrote: >I'm not entirely familiar with PCA and could use some help. > >I've used PCA w/varimax rotation to reduce 10 variables (answers to a racism >attitudes questionnaire) down to 2 factors. I want to know if the >calculated factor scores for each participant can then be used as a >dependent variable in subsequent analyses, or whether I should simply >combine the variables loading on the respective factors and use those? My >problem is in interpreting the factor scores: Group 1 has a mean of -2.72 >and Group 2 has a mean of 2.68. These are significantly different, but I'm >not sure what the means represent (the raw data are scores ranging from 1 to >10, so there are no negatives). > >Thanks for any insight. > >Fred Rose > > > > |
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This was very helpful. To answer your question: Participants viewed images
of couples that were/were not interracial and answered several questions. The first factor seemed related to a situational interpretation (e.g., judgments about the couple's happiness, etc.) while the second was about more innate racist attitudes (willingness to have the couple over for dinner, etc). The questions were mixed in wording but we reversed scored several so that higher scores always meant more positive attitudes. I have two questions: 1. How can I find out what "end" of the scale my groups are on? Just look at the group means of the scales? What is interesting is that the groups who viewed same-race couples (white-white or black-black) had the negative scores on factor 1, while the mixed race groups had positive scores. I'm curious to know if this means the same race groups reported LESS positive attitudes towards the couples than the mixed race groups. 2. When you say " it is traditional to calculate scale scores by summing items, reflecting those items that have negative weights" what did you mean by reflecting those items that have negative weights? Reverse score items that load negatively on that factor? Thanks for your explanation. Most of the readings I have don't say anything more about factor scores other than they can be used in plots. Fred On 11/15/06 6:07 AM, "Art Kendall" <[hidden email]> wrote: > You can use the factor scores in any design role. > Think of the factor scores as z-scores. Mean of zero, SD of 1. > > What interpretation did you give to the two factors? Are the factors > bipolar or unipolar? > > If you have 2 groups of respondents, and the mean factor scores you > mention are for these groups, then group 1 is at one end of the scale > and group 2 is at the other. The direction of factors is completely > arbitrary. > > When developing scales, it is traditional to calculate scale scores by > summing items, reflecting those items that have negative weights. > Since reliability, correlations etc. are not changed by dividing by a > constant, you might want to work with a mean of the items. > > It is also possible that you would want to reflect one or both scales so > that the high end is meaningful, e.g., high scores mean more racism. > The choice of direction is usually made to make correlations, etc., with > other variables have less complex verbal explanations. > > Art Kendall > Social Research Consultants > > > Fredric E. Rose wrote: > >> I'm not entirely familiar with PCA and could use some help. >> >> I've used PCA w/varimax rotation to reduce 10 variables (answers to a racism >> attitudes questionnaire) down to 2 factors. I want to know if the >> calculated factor scores for each participant can then be used as a >> dependent variable in subsequent analyses, or whether I should simply >> combine the variables loading on the respective factors and use those? My >> problem is in interpreting the factor scores: Group 1 has a mean of -2.72 >> and Group 2 has a mean of 2.68. These are significantly different, but I'm >> not sure what the means represent (the raw data are scores ranging from 1 to >> 10, so there are no negatives). >> >> Thanks for any insight. >> >> Fred Rose >> >> >> >> > -- Fredric E. Rose, Ph.D. Assistant Professor of Psychology Palomar College (760) 744-1150 x2344 [hidden email] |
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It will be easier to interpret results if you use the traditional scale
construction. By seeing which items load say |.40|, you can see if they form bipolar or unipolar scales. If you send me the rotated loadings and 10 SPSS variable names with the items, I'll put together a snippet of syntax. A concrete example might be more communicative than a string of hypotheticals. Did each participant view more than one image? if so how did you handle that in the factor analysis? Do you have an ad hoc instrument or is it a widely used one? Art Kendall Social Research Consultants Fredric E. Rose, Ph.D. wrote: >This was very helpful. To answer your question: Participants viewed images >of couples that were/were not interracial and answered several questions. >The first factor seemed related to a situational interpretation (e.g., >judgments about the couple's happiness, etc.) while the second was about >more innate racist attitudes (willingness to have the couple over for >dinner, etc). > >The questions were mixed in wording but we reversed scored several so that >higher scores always meant more positive attitudes. > >I have two questions: > >1. How can I find out what "end" of the scale my groups are on? Just look >at the group means of the scales? What is interesting is that the groups >who viewed same-race couples (white-white or black-black) had the negative >scores on factor 1, while the mixed race groups had positive scores. I'm >curious to know if this means the same race groups reported LESS positive >attitudes towards the couples than the mixed race groups. > >2. When you say " it is traditional to calculate scale scores by >summing items, reflecting those items that have negative weights" what did >you mean by reflecting those items that have negative weights? Reverse >score items that load negatively on that factor? > >Thanks for your explanation. Most of the readings I have don't say anything >more about factor scores other than they can be used in plots. > >Fred > > >On 11/15/06 6:07 AM, "Art Kendall" <[hidden email]> wrote: > > > >>You can use the factor scores in any design role. >>Think of the factor scores as z-scores. Mean of zero, SD of 1. >> >>What interpretation did you give to the two factors? Are the factors >>bipolar or unipolar? >> >>If you have 2 groups of respondents, and the mean factor scores you >>mention are for these groups, then group 1 is at one end of the scale >>and group 2 is at the other. The direction of factors is completely >>arbitrary. >> >>When developing scales, it is traditional to calculate scale scores by >>summing items, reflecting those items that have negative weights. >>Since reliability, correlations etc. are not changed by dividing by a >>constant, you might want to work with a mean of the items. >> >>It is also possible that you would want to reflect one or both scales so >>that the high end is meaningful, e.g., high scores mean more racism. >>The choice of direction is usually made to make correlations, etc., with >>other variables have less complex verbal explanations. >> >>Art Kendall >>Social Research Consultants >> >> >>Fredric E. Rose wrote: >> >> >> >>>I'm not entirely familiar with PCA and could use some help. >>> >>>I've used PCA w/varimax rotation to reduce 10 variables (answers to a racism >>>attitudes questionnaire) down to 2 factors. I want to know if the >>>calculated factor scores for each participant can then be used as a >>>dependent variable in subsequent analyses, or whether I should simply >>>combine the variables loading on the respective factors and use those? My >>>problem is in interpreting the factor scores: Group 1 has a mean of -2.72 >>>and Group 2 has a mean of 2.68. These are significantly different, but I'm >>>not sure what the means represent (the raw data are scores ranging from 1 to >>>10, so there are no negatives). >>> >>>Thanks for any insight. >>> >>>Fred Rose >>> >>> >>> >>> >>> >>> > >-- >Fredric E. Rose, Ph.D. >Assistant Professor of Psychology >Palomar College >(760) 744-1150 x2344 >[hidden email] > > > > |
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