Interpretation of factor analysis using SPSS

We have already discussed about factor analysis in the previous article (Factor Analysis using SPSS), and how it should be conducted using SPSS. In this article we will be discussing about how output of Factor analysis can be interpreted.

Descriptive statistics

The first output from the analysis is a table of descriptive statistics for all the variables under investigation. Typically, the mean, standard deviation and number of respondents (N) who participated in the survey are given. Looking at the mean, one can conclude that respectability of product is the most important variable that influences customers to buy the product. It has the highest mean of 6.08 (Table 1).

Table 1
Table 1: Descriptive statistics

The correlation matrix

The next output from the analysis is the correlation coefficient. A correlation matrix is simple a rectangular array of numbers which gives the correlation coefficients between a single variable and every other variables in the investigation. The correlation coefficient between a variable and itself is always 1, hence the principal diagonal of the correlation matrix contains 1s (See Red Line in the Table 2 below). The correlation coefficients above and below the principal diagonal are the same. The determinant of the correlation matrix is shown at the foot of the table below.

With respect to Correlation Matrix if any pair of variables has a value less than 0.5, consider dropping one of them from the analysis (by repeating the factor analysis test in SPSS by removing variables whose value is less than 0.5). The off-diagonal elements (The values on the left and right side of diagonal in the table below) should all be very small (close to zero) in a good model.

Table 2: Correlation matrix
Table 2: Correlation matrix

Kaiser Meyer Olkin (KMO) and Bartlett’s Test (measures the strength of relationship among the variables)

The KMO measures the sampling adequacy (which determines if the responses given with the sample are adequate or not) which should be close than 0.5 for a satisfactory factor analysis to proceed. Kaiser (1974) recommend 0.5 (value for KMO) as minimum (barely accepted), values between 0.7-0.8 acceptable, and values above 0.9 are superb. Looking at the table below, the KMO measure is 0.417, which is close of 0.5 and therefore can be barely accepted (Table 3).

There is no significant answer to question “How many cases respondents do I need to factor analysis?”, and methodologies differ. A common rule is to suggest that a researcher has at least 10-15 participants per variable. Fiedel (2005) says that in general over 300 Respondents for sampling analysis is probably adequate. There is universal agreement that factor analysis is inappropriate when sample size is below 50.

Bartlett’s test is another indication of the strength of the relationship among variables. This tests the null hypothesis that the correlation matrix is an identity matrix. An identity matrix is matrix in which all of the diagonal elements are 1 (See Table 1) and all off diagonal elements (term explained above) are close to 0. You want to reject this null hypothesis. From the same table, we can see that the Bartlett’s Test Of Sphericity is significant (0.12). That is, significance is less than 0.05. In fact, it is actually 0.012, i.e. the significance level is small enough to reject the null hypothesis. This means that correlation matrix is not an identity matrix.

Table 3: KMO and Barlett's test
Table 3: KMO and Barlett’s test

Communalities

The next item from the output is a table of communalities which shows how much of the variance (i.e. the communality value which should be more than 0.5 to be considered for further analysis. Else these variables are to be removed from further steps factor analysis) in the variables has been accounted for by the extracted factors. For instance over

90% of the variance in “Quality of product” is accounted for, while 73.5% of the variance in “Availability of product” is accounted for (Table 4).

Table 4: Communalities
Table 4: Communalities

Total variance explained

Eigenvalue actually reflects the number of extracted factors whose sum should be equal to number of items which are subjected to factor analysis. The next item shows all the factors extractable from the analysis along with their eigenvalues.

The Eigenvalue table has been divided into three sub-sections, i.e. Initial Eigen Values, Extracted Sums of Squared Loadings and Rotation of Sums of Squared Loadings. For analysis and interpretation purpose we are only concerned with Extracted Sums of Squared Loadings. Here one should note that Notice that the first factor accounts for 46.367% of the variance, the second 18.471% and the third 17.013%. All the remaining factors are not significant (Table 5).

  1. Component: As can be seen in the Communalities table 3 above, there 8 components shown in column 1 under table 3.
  2. Initial Eigenvalues Total: Total variance.
  3. Initial Eigenvalues % of variance: The percent of variance attributable to each factor.
  4. Initial Eigenvalues Cumulative %: Cumulative variance of the factor when added to the previous factors.
  5. Extraction sums of Squared Loadings Total: Total variance after extraction.
  6. Extraction Sums of Squared Loadings % of variance: The percent of variance attributable to each factor after extraction. This value is of significance to us and therefore we determine in this step that they are three factors which contribute towards why would someone by a particular product.
  7. Extraction Sums of Squared Cumulative %: Cumulative variance of the factor when added to the previous factors after extraction.
  8. Rotation of Sums of Squared Loadings Total: Total variance after rotation.
  9. Rotation of Sums of Squared Loadings % of variance: The percent of variance attributable to each factor after rotation.
  10. Rotation of Sums of Squared Loadings Cumulative %: Cumulative variance of the factor when added to the previous factors.
Table 5: Total variance
Table 5: Total variance

Scree plot

The scree plot is a graph of the eigenvalues against all the factors. The graph is useful for determining how many factors to retain. The point of interest is where the curve starts to flatten. It can be seen that the curve begins to flatten between factors 3 and 4. Note also that factor 4 onwards have an eigenvalue of less than 1, so only three factors have been retained.

Figure 1: Screen plot
Figure 1: Scree plot

Component matrix

The table 6 below shows the loadings (extracted values of each item under 3 variables) of the eight variables on the three factors extracted. The higher the absolute value of the loading, the more the factor contributes to the variable (We have extracted three variables wherein the 8 items are divided into 3 variables according to most important items which similar responses in component 1 and simultaneously in component 2 and 3). The gap (empty spaces) on the table represent loadings that are less than 0.5, this makes reading the table easier. We suppressed all loadings less than 0.5 (Table 6).

Table 6: Component matrix
Table 6: Component matrix

Rotated component matrix

The idea of rotation is to reduce the number factors on which the variables under investigation have high loadings. Rotation does not actually change anything but makes the interpretation of the analysis easier. Looking at the table below, we can see that availability of product, and cost of product are substantially loaded on Factor (Component) 3 while experience with product, popularity of product, and quantity of product are substantially loaded on Factor 2. All the remaining variables are substantially loaded on Factor. These factors can be used as variables for further analysis (Table 7).

Table 7: Rotated component matrix
Table 7: Rotated component matrix
Factor analysis using SPSSCorrelation of variables in SPSS

Priya Chetty

Partner at Project Guru
Priya is a master in business administration with majors in marketing and finance. She is fluent with data modelling, time series analysis, various regression models, forecasting and interpretation of the data. She has assisted data scientists, corporates, scholars in the field of finance, banking, economics and marketing.
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59 thoughts on “Interpretation of factor analysis using SPSS”
  1. Avatar sankari 4 years ago

    We have lot of tables in factor analysis. but which is placed in the dissertation.

  2. Avatar sankari 4 years ago

    This content is very useful. But i have one doubt. We have lot of tables in factor analysis. but which is placed in the dissertation.

  3. Avatar kaveri 3 years ago

    this artical is very useful, but i have more doubt. enoda project factor analysis podu iruken mam,athu la interpretation mattum correct ta pathu solunga mam plzz..

  4. Avatar Daniel Frimpong 3 years & 3 months ago

    which table is constructed in the dissertation. please help me out. how do I construct a factor analysis table in my dissertation.

    • Avatar Shruti Datt 3 years & 3 months ago

      Mr. Daniel,
      There are different tables which are obtained during factor analysis, however the most important is the rotated component matrix which reflects on the key factors which are contributing towards your research.

  5. Avatar sharada 3 years & 1 month ago

    how to write interpretation for factor analysis?I am doing Ph.d in english. I have chosen factor analysis for my questionnaire. I will provide u one question. let me know how to interpret it. for instance there are some questions on English language competency for students. for example, I have good pronunciation, good vocabulary which come under one factor. then I have proper grammatical knowledge and proper punctuation knowledge which come under second factor and I am good at spellings come undr third variable. How to use these factors for interpretation? Please let me know this?

  6. Avatar Shruti Datt 3 years & 1 month ago

    Dear Sharada,

    This article discusses the interpretation of different tables and graphs obtained using factor analysis. In order to further understand how one can interpret results from factor analysis, you can seek guidance from us. Or you can opt for a new order with us to work on your research analysis.

  7. Avatar Sachin 3 years ago

    Hi Priya/Shruti,

    Greetings!

    This is Sachin.

    I am based in Sydney and I conduct face to face tuitions. Quite a few of my students need backend support for SPSS assignments.

    Is it something of interest for you ladies?

    Please let me know..

    Thanks & regards,

  8. Avatar Shruti Datt 3 years ago

    Dear Mr. Sachin,

    Greetings!
    Surely we can help you with same. You can mail me the details and we can carry this forward.

    Best Regards:
    Shruti Datt

    ([email protected])

  9. Avatar Soheyb 3 years & 3 weeks ago

    Thank you for your informing article. I’ve got a question regarding “rotated component matrix”: there are times when items load on more than one factor, for example, item ” experience with product” has loaded on both factors 1 and 2. Should we exclude that item or what? As far as I know items that load on more than one factor with item loadings greater than .30 should be excluded from the analysis. I’ll appreciate that if you could explain more on that.
    Thanks in advance.

  10. Avatar Shruti Datt 3 years & 3 weeks ago

    Dear Soheyb,
    More often, the items which load on more than 1 factor are removed from the analysis. Firstly, because this item is confusing for the respondent and thus can’t be added to any of the factor category. Secondly, once these items are removed we get non-ambiguous questionnaire.
    I hope this helps.

    You may also opt for Training and personal assistance sessions with us.

  11. Avatar Nayani 3 years & 2 weeks ago

    Hi!
    I didn’t get extraction column in communalities table in my output ..why is that ?

  12. Avatar Rishav Sharma 2 years & 10 months ago

    hello,
    Ian doing my thesis work so i adopted the factor. i had 37 factors in my analysis in the form of variable and rest the data in data sheet. I am not able to understand the interpretation of the data and which factors are important

    • Avatar Shruti Datt 2 years & 10 months ago

      Dear Rishav,
      The 37 statements will be segregated into different columns in the rotated component matrix. The statements in the first column will be most important and will come under one variable.
      The results should be presented diagonally based on the column which they appear.

      You may also opt for Training and personal assistance sessions with us.

  13. Avatar sundari 2 years & 9 months ago

    hello
    i am doing the project my tittle is to predict the buying trend of consumer for fruits vegetables and grocery items how i interpret the our factor analysis

    • Avatar Shruti Datt 2 years ago

      Dear Sundari,

      We can evaluate your questionnaire and analysis to determine the issues with your analysis. You can seek personal assistance for same.

  14. Avatar Lizzy zinyemba 2 years ago

    l need assistance on factor analysis interpretation of data

  15. Avatar jonx 2 years ago

    hi can the eigenvalue of kaiser criterion be changed other than the default value?

    • Avatar Shruti Datt 2 years ago

      Dear Jonx,
      Thanks for the query.
      Yes, we can change the default value to less or more than 1.
      Otherwise, depending on the factors you need, you can change the no of factors to be extracted as well.

  16. Avatar Iesha 2 years & 3 months ago

    Hi
    there r certain queries related to values in rotated component matrix….

    1. Is it fine to get say 12 factors in Rotated Component Matrix with none of the items/statements under one or more factors. Should we in that case consider rest of the factors or some sort treatment is needed.

    2. in case an item falls under 2 or more factors, should we consider it under the one with highest value.??

    3. in case there are one or two statements that come under a factor in rotated component matrix, but logically we find that those two can be included in some other factor, should we merge them or what else can be done in such a case.??

    thanks in advance 🙂

    • Avatar Shruti Datt 2 years ago

      Dear Iesha,
      Greetings!
      You have raised valid points for your analysis, however, you should not focus only on the Rotated Component Matrix. Rather you need to review the Eigen Values and the Scree Plot as well.
      Please find below the answers to your queries below:

      1. These 12 factors are individual factors with sub-factors under them? The factors which are not coming under any factor can be removed from the final likert scale.

      2. Yes, it is advisable to chose the one with highest value.

      3. Yes, in case the factor is similar then they can be merged under bigger factor.

      • Avatar Iesha 2 years ago

        Hi Shruti..

        Thanks a lott 🙂

        in case we r getting some factors containing 2-3 random items (i.e., which are logically quite different from rest of the items in a factor), what kind of treatment should be done. I mean how can we assess where the problem lies, if even after increasing the sample size situation remains the same.

      • Avatar Shruti Datt 2 years ago

        Dear Iesha,
        Mostly when people respond similarly to set of statements in one factor they are grouped as one factor in the matrix.
        So, you check the mean/descriptives of these individual statements to know if all the individuals are pointing at the same thing. If not then these statements should be excluded.

  17. Avatar Iesha 2 years ago

    hi
    this is regarding choice of EFA vs CFA..

    what I know as per my knowledge is that when we are working on something which has no literature available and make statements with the help of experts, we employ EFA.. and if we literature is available and there are standardised scales or we modify (add/delete) items .. we employ CFA…

    now I am working on something where a model has been proposed by the authors previously. so I am having the constructs available, but they have used hardly 5-6 items per construct… I, with the help of literature, have gathered or say modified a no. of statements for each construct (approx 50 statements per construct)..

    now, for analysis part should I start with EFA or apply directly CFA… and wat for pilot study data.??? please help with this 🙂

    • Avatar Shruti Datt 2 years & 2 months ago

      Hi,
      You will have to start with EFA and then apply CFA.
      EFA will be applied on the pilot data only. Based on the findings of Pilot results, the final analysis will be done using CFA.

      I hope this helps.

  18. Avatar Iesha 2 years & 2 months ago

    thanks a lot Shruti for guiding 🙂
    But actually few experts mention that EFA is applied for a study where no previous work is available and we make statements with the help of experts and our own understanding of the things.. and CFA is applied in case we have literature available with us and we use it as it is or with certain modifications…

    Please clarify on this..

    • Avatar Shruti Datt 2 years & 2 months ago

      Hi,
      For your study only I am stating that you will have to apply EFA first and then apply CFA. Although you have some statements, but you have will have establish their validity first. Both using EFA and other tools like chi square, goodness of fit etc.

  19. Avatar Iesha 2 years & 2 months ago

    thanks a lot Shruti.. You have been a great help 🙂

  20. Avatar William Pascal 2 years & 2 months ago

    Hello Shruti Dati
    In the rotated component matrix, what is considered to select the variables to be used? Im confused whether we i should choose those with higher loading from each category or i choose any with high loading regardless of its category

    • Avatar Shruti Datt 2 years & 2 months ago

      Dear William,

      Generally, the variables which are under same category i.e. main factor are presented in one column and would have similar values. But in case they are segregated then you should pick the one with higher loading for that particular category as per the literature.

  21. Avatar Iesha 2 years ago

    hi..
    plz help me with one thing.. what I have learnt till now is that we apply single EFA on our questionnaire.. But I feel it is correct when we have a number of items in a single construct.. and when there are 3-4 different (logically) constructs, EFA should be applied separately.. please clarify on this..

    • Avatar Chandrika Kapagunta 2 years ago

      Hi Lesha,
      I agree with you. The purpose of EFA or CFA is to confirm which of the items represent a construct best, based on your data. Therefore, EFA has to be performed on each of the logically different construct separately. This way you will know which items you will need to keep, and which ones have to be dropped.

      I hope this has helped.

      • Avatar Iesha 2 years & 1 month ago

        Thanks a lot Chandrika 🙂 one more thing is there… CFA is applied on a model as a whole and not on constructs.. Plz correct me on this if I am wrong.. and considering the same case as mentioned before, should we proced like applying EFA on individual constructs and CFA on whole model… or CFA also individually..
        Thanks in advance..
        Regards
        Iesha

      • Avatar Iesha 2 years & 1 month ago

        Hello Shruti..
        can u plz help me with my query mentioned..
        Thanks and Regards

  22. Avatar ayu 2 years ago

    Hi Shruti,
    do we need to do again factor analysis using the latest items after we removed the items that should be removed?

    • Avatar Avishek Majumder 1 year ago

      Hi Ayu,
      Good day!
      Yes, it is important that you re-perform factor analysis even after removing variables as the loadings and other parameters changes after every deletion.

  23. Avatar Pawan joshi 1 year & 8 months ago

    Good morning ma’am
    There is a query from my side that in total variance explained table how to know that which variable is there whose value is greater than 1 as spss giving components 1,2,3…
    How to know that what are those factors/ components whose eigen value greater than 1 .
    For example in the total variance table explained by you in above…
    How we came to know that these 3 factors which are extracted what are these 3 components whose Eigen value greater than one..
    I’ll be highly obliged please let me know..
    Pawan Joshi

    • Avatar Avishek Majumder 1 year ago

      Hi Pawan,
      Greetings of the day!
      As in the total variance table, you can see that the first three values have greater than 1. The component sequence follows the same sequence of communalities table. So 1 will be the availability of a product.

  24. Avatar Karanpreet kaur 1 year ago

    Mam what is meant by high loading in factor analysis??

    • Avatar Prateek Sharma 1 year ago

      Hi Karanpreet,

      Hope you’re doing well.

      “Loading” basically refers to the weights of each variable in respect to the factors we’re creating. All the variables may or may not show the degree of their belonging to all the factors. However, these variables show high loading weights to the underlying factors they belong to. And in order to get a clear picture, Rotated Component Matrix arranges the variable in a way that most belonging variable will come at the top of each factor with their High Loading weights.

  25. Avatar Karanpreet Kaur 1 year ago

    Thank u mam for this information .It helps a lot in understanding factor analysis.

    Mam my query is
    In interpretation, I studied that we have to calculate factor score and if not want to calculate then select surrogate variable ..mam plz explain this

    • Avatar Prateek Sharma 1 year ago

      Hi,

      Surrogate variables are just the ones which define the significance of each factor based on their high weights. We select these variable/s so as to reduce the dimension while still keeping the original significance of it.

  26. Avatar Sonia 1 year & 6 months ago

    Hi,
    I am doing an EFA and I need to know if there is lower communalities do you remove that first or the cross loading item. I followed the procedure check KMO, Bartletts test, communalities and then Pattern Matrix.

    • Avatar Sudeshna 1 year & 6 months ago

      Hey Sonia,

      If you see any item cross loading, see the items, if the communality is less than 0.5, try removing those items from further analysis. Remember that the deletion of the items should not affect the Factor theoretically. It should be theoretically justified. If the item is important and its deletion can affect the content validity of the construct, you may need to retain it.

  27. Avatar Ma 1 year & 4 months ago

    hi
    I’m doing CFA using Amos, my fit indices are weak, I’m suggested performing EFA and prepare good data for CFA ( removing all items that cause problems in model fit). after reading many videos, I can run EFA but my big issue is that I can’t be able to interpret EFA results ( how to know those items that cause problems in my model) Can you help me please on the hint. I also have 4 constructs with 44 items, should I run EFA for whole constructs or individual construct?
    thank you so much in advance

    • Avatar Sudeshna Chakraborty 1 year & 4 months ago

      Hello Ma,

      Although I am not sure about your study aim or its variables, still in a generic sense, running EFA on 44 items/factors will help you narrow down the items/factors with highest loadings. The ones with the highest loadings will further be analysed using CFA.

      So, to answer your query on how to know the items problematic- you should identify them with the factor loadings given in Factor Matrix, Pattern Matrix and Structure Matrix tables.
      Factor loadings help you understand the relationship (correlation coefficient) between a symptom/dimension and a factor/item.

      Hope this helps and do let us know!

  28. Avatar Ayesha Rehman 1 year & 3 months ago

    can anyone help me that after running EFA Test I got 13 factors. I used 44 questions in my questionnaire so now have to extract some questions so how to decide which questions should I extract.

  29. Avatar Ashwani 1 year & 3 months ago

    Hi,
    i need a help regarding PCA . In the Rotated Matrix, there is only one Variable which is getting loaded on 5th factor, with a high value of 0.888 ( the variables of same category are loaded on factor 3rd), what do i do in this case.

  30. Avatar Ashwani 1 year & 3 months ago

    anybody there to help? i would appreciate an early solution. i am stuck with this last portion.

  31. Avatar abbas 1 year ago

    hello dear
    Please tell me about the loading factor and how to analyze it in spss

  32. Avatar Asma' Ismail 8 months & 2 weeks ago

    Hello, i need to know from which part i should removed my variable. Based on the value in rotated componet matrix or component matrix?

  33. Avatar Ekta 8 months & 2 weeks ago

    Hi!
    All those variables which do not have high factor loadings (generally < 0.5) and are out from the groups of variables appearing in pattern matrix, are excluded from the research study. In fact you can suppress the values below 0.5 at the time when you run this code Analyze-> Dimension reduction-> Options-> Suppress

  34. Avatar asad 8 months & 2 weeks ago

    thank you for your inforayion

  35. Avatar Tony 7 months & 2 weeks ago

    Hi i was task to do a research on customer satisfaction on water quality, i am completely lost on how to interpret the data i get from Factor Analysis….please help

  36. Avatar Badi, Lwidiko 6 months & 3 weeks ago

    Hi! I am stuck I run EFA for three constructs with 25 items. The output in a rotated matrix formed five components of which some items from construct 2 moved to component 3 and those in construct 3 separated to component 4 and 5. Can i remove those items in component 4 and 5? anyone who can assist me as early as possible to rescue me from high jam

  37. Avatar Divya 6 months & 2 weeks ago

    Hi Badi , Lwidiko

    Items of the construct 3 can be moved upon component 4 or 5 if the attributes associated with the construct 3 is related to the component 4 or 5. This is because each construct contains the items with the similar set of attributes. In addition to this , each construct explains the extent of similarity of responses to the items within different constructs.
    For instance , if there are three constructs: competence , satisfaction and motivation among the employees. Factor analysis would help in examining the extent to which the responses related to motivation are linked with competence items and so on. Thus , items of construct 3 can be separated to component 4 or 5 depends upon the attributes on which these items are based.

  38. Avatar krutarth 6 months ago

    I have 22 statements of factor analysis. everything is done on SPSS just the thing is that i am getting two components tables.so which component table i should analyize and interpretate

  39. Avatar Divya Narang 5 months & 3 weeks ago

    Hi Krutarth,

    In a factor analysis, there are two types of component matrix which are represented in the form of tables, the first is the rotated component matrix and other one is the component matrix or the unrotated component matrix. The rotated component analysis represent the factor loading of the principal components analysis that represents the correlation among the variables.Through the rotation matrix , we can reduce the number of factors on which the variables have high factor loading. On the other hand , the component matrix represent the extent to which each factor contributes the variable. So, the component matrix which is to be used depends on the extent of data, variables and objectives.

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