I want to run a Mixed ANOVA in SPSS. I have two levels of between-subjects factors (i.e., group membership), and eight levels of within-subjects factors (eight timepoints) at which subjects were measured.
The problem is that most subjects skipped at least one (and often several) timepoints and therefore do not have measurements at those timepoints.
When I used the Mixed Anova procedure in SPSS, it did the procedure but only used a fraction of my cases. It only used the few subjects who had measurements at all eight timepoints. It used so few subjects that the analysis is not valid. Is there a way around this? I'm thinking of imputing missing values (possibly using last known value, or regression substitution, or an average for all subjects at that timepoint), or maybe eliminating some timepoints that most subjects seem to have missed, but that still would eliminate some subjects from the analysis. I've heard of "robust mixed ANOVA" which sounds like it might handle missing data. Any advice appreciated. (note that I'm not doing simple repeated-measures ANOVA on one group; I have two groups).
One approach is to restructure the data from WIDE to LONG (via VARSTOCASES command), and then use the MIXED procedure to estimate the model. Here's an example from textbook author David Howell's website (see link below):
MIXED
dv BY Group Time
/CRITERIA = CIN(95) MXITER(100) MXSTEP(5) SCORING(1)
SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(0,
ABSOLUTE)
PCONVERGE(0.000001, ABSOLUTE)
/FIXED = Group Time Group*Time | SSTYPE(3)
/METHOD = REML
/PRINT = DESCRIPTIVES SOLUTION
/REPEATED = Time | SUBJECT(Subject) COVTYPE(CS)
/EMMEANS = TABLES(Group)
/EMMEANS = TABLES(Time)
/EMMEANS = TABLES(Group*Time) .
IIRC, this approach assumes the data are MAR--i.e., missing at random.
HTH.
EDITED 3-Jun-2015
Someone pointed out to me a small but important error in Howell's syntax shown above. If you download his data and try to run that MIXED command, you'll have to change Subject to Subj on the REPEATED sub-command. I.e., change this:
/REPEATED = Time | SUBJECT(Subject) COVTYPE(CS)
to this:
/REPEATED = Time | SUBJECT(Subj) COVTYPE(CS)
This is because the unique identifier variable in Howell's data file is called Subj, not Subject.
http://www.uvm.edu/~dhowell/StatPages/More_Stuff/Mixed-Models-Repeated/Mixed-Models-for-Repeated-Measures1.html
One approach is to restructure the data from WIDE to LONG (via VARSTOCASES command), and then use the MIXED procedure to estimate the model. Here's an example from textbook author David Howell's website (see link below):
MIXED
dv BY Group Time
/CRITERIA = CIN(95) MXITER(100) MXSTEP(5) SCORING(1)
SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(0,
ABSOLUTE)
PCONVERGE(0.000001, ABSOLUTE)
/FIXED = Group Time Group*Time | SSTYPE(3)
/METHOD = REML
/PRINT = DESCRIPTIVES SOLUTION
/REPEATED = Time | SUBJECT(Subject) COVTYPE(CS)
/EMMEANS = TABLES(Group)
/EMMEANS = TABLES(Time)
/EMMEANS = TABLES(Group*Time) .
IIRC, this approach assumes the data are MAR--i.e., missing at random.
HTH.
EDITED 3-Jun-2015
Someone pointed out to me a small but important error in Howell's syntax shown above. If you download his data and try to run that MIXED command, you'll have to change Subject to Subj on the REPEATED sub-command. I.e., change this:
/REPEATED = Time | SUBJECT(Subject) COVTYPE(CS)
to this:
/REPEATED = Time | SUBJECT(Subj) COVTYPE(CS)
This is because the unique identifier variable in Howell's data file is called Subj, not Subject.
http://www.uvm.edu/~dhowell/StatPages/More_Stuff/Mixed-Models-Repeated/Mixed-Models-for-Repeated-Measures1.html
Bruce, your solution is valid and I think both "intent-to-treat" and transforming the data so the group by time is fixed should be used. There may be a difference between the groups in their skipping patterns which could have a clinical significance. I think Jerry should report the data based on "intent-to-treat" and then present additional analysis where data is MAR.
As an aside, when you move to using MIXED, strongly consider treating time points as continuous if your intervals are approximately equal. This will buy you both simplicity (you're only testing a slope difference across groups) and power.
Hi Jerry - important first step is to establish whether those missing values are missing at random or systematically. You mentioned that there are some that are more likely missing than others. Intention to treat strategies of all kinds are based on the assumption that these values are randomly missing; not a result of gender or location, etc.
All of the method you and others have mentioned are valid ways to treat missing data. It's important to think through the logic of each to determine which is best in your circumstance and for your subjects. For instance:
1) last value carried forward is an assumption that subjects are more likely to change over longer periods of time and that nearer period differences are not that important
2) averaging the subjects values on either side of the missing value assumes that changes happen fairly linearly - not true for all kinds of data
3) Using the average group change is a very conservative estimate of change but in datasets with many missing values average substitution tends to reduce the variability and can have an effect on the ability to find significant differences
What's perhaps most important is to recognize that most measures are not indicative a the "True Score" but are themselves approximations. Using thoughtful approximations/substitutions of missing values do not in themselves diminish the value of your data.
Having said that, it's good practice to be sure that your strategy had not skewed results by doing a comparison (if possible) of complete subjects data to modified data to see if there are significant differences on variables you consider important to your study.
Good luck
Thank you Robert! It is a difficult decision as to which approach to take. I like the possibility of averaging the values on either side of the missing data, because the changes over time (in my variable of interest) actually are fairly linear. I'm exploring the method of substituting missing values with values predicted from multiple linear regression (using two other variables) across the whole time period, but this is made complicated by the fact that that relationship is not always linear . . . although I understand that this assumption (of linearity in regression) is often not met and the analysis is done anyway. I'm still exploring.
Best of luck - remember, whatever you decide, you'll need to be fairly transparent about when you describe your research. You needn't be exhaustively precise, but you'll need to indicate in gross terms what you did.
Hello Jerry and all,
I was wondering if you utilized the mixed model for your purpose and whether it did work? I am facing the same issue right now as I am trying to see how can I use mixed model to solve for two within factors and one between factor for my research. I really appreciate if you let me know if the suggested approach here worked for you or not.
Mainly, I am wondering how do you specify that a factor is between as opposed to within. My approach was to use within factors (SR and Eyes) as repeated and left the between factor (health condition) out. and then ran the full factorial with all three factors. I suppose that SPSS understands that my between factor (health condition) is not a repeated factor. I will really appreciate if anyone can share your thoughts on that. Here is my syntax:
MIXED EnHL_ML BY HealthCond SR Eyes
/CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0,
ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE)
/FIXED=HealthCond SR Eyes HealthCond*SR HealthCond*Eyes SR*Eyes HealthCond*SR*Eyes | SSTYPE(3)
/METHOD=REML
/PRINT=DESCRIPTIVES SOLUTION
/REPEATED=SR*Eyes | SUBJECT(id) COVTYPE(DIAG)
/EMMEANS=TABLES(HealthCond) COMPARE ADJ(LSD).
- Badges
- Science method
- Similar topics
- Mathematics
- Statistics
- Statistical Modeling
- Analyses of Variance
- ANOVA