Whatever I was going to do productive on the plane was interrupted by me reading Sh*t My Dad Says. This convinced me that I will never be a best-selling author because I will NEVER be that funny. The book is hilarious. Read it.
Thankfully for me the book was so funny that it was either quit reading or laugh so loudly I would wake up the passenger next to me. Thankful because I needed to get some work done. I’m in North Dakota where I will spend three days on a site visit to a program and then another couple of days meeting with teachers and school administrators about 7 Generation Games.
Speaking of books, even though we temporarily weren’t, I’ve been speaking with Darling Daughter Number One about co-authoring a book on parenting next year. She likes the title The Dragon Mother. Darling Daughter Number Three likes The Komodo Mother (going along with the dragon motif) . My personal pick would be How You Like Me Now?
Having one book on the market that is selling respectably well (Winning on the Ground – it’s on knocking people down, choking them and breaking their arms) I am well aware of the fact that while writing may be an art, publishing is most definitely a business. No doubt the title is going to be decided based on a focus group or some other means of determining what is going to sell.
Another book that I started on and have yet to finish was on statistics and a naked mole rat. There are a whole lot of statistics textbooks and academic journals on statistics or with statistical results. There is not to my knowledge a book of someone just rambling on with statistical shit thrown in there, plus a naked mole rat. Like Malcolm Gladwell but with more statistics, more swearing, probably worse writing, but I will have a naked mole rat (which he does not) and if I do happen to discuss eigenvalues I will spell the word correctly.
Maria and I have kicked around the idea of taking some posts from this blog and turning it into a book, particularly the ones on 55 things I have learned.
Whatever book I write next will almost definitely be done with a mainstream, traditional publisher because of an experiment I did a couple of years ago.
Many years ago, when I was traveling to North Dakota a lot, before any Internet except for AOL on dial-up, I was pretty bored in the evenings. I could only fit so many books in my suitcase and there was only one bookstore within 100 miles, then it closed and there were none. So, while I was sitting inside avoiding the snow, I wrote three books – I don’t know why, I guess because I can’t knit. I published one on Smashwords and the same book on Amazon , because I still hadn’t decided yet whether I was going to self-publish my judo book or go with a traditional publisher. What I discovered was that if you want to sell books that way you have to get out and promote them, write blogs about them , tweet about them to the point of being irritating. Otherwise, you sell about one book a month.
So, I went with Black Belt for my judo book and it is now #1 on Amazon in the mixed martial arts category, #7 in martial arts and from #17,000 – #48,000 or so out of the over one million books they sell.
You see, I don’t LIKE doing any of that marketing stuff and I like the work I do. I don’t have any mad passion to be A WRITER like all of those people who say, “If I couldn’t write, I’d die.”
If I couldn’t write, I’d probably learn to knit.
I’ve been thinking about this a lot lately. It started when I read an article by David Brooks where he actually gave a student at Yale an ‘A’ and approved her assessment that
“Time not spent investing in yourself carries an opportunity cost, rendering you at a competitive disadvantage as compared to others who maintained the priority of self.”
I found that appalling. The link doesn’t go back to Brooks’ originally article. I already did that once in my prior post. I don’t want to encourage him.
Equally appalling was the comment I heard on National Public Radio (NPR) this week when discussing the bridge collapse in Seattle. The commentator was interviewing someone who said that we actually knew about structural problems in thousands of bridges across the country but no one wanted to vote for repairs during his/ her term in office. The interviewer laughed and said,
Isn’t that just human nature? We all want benefits but we don’t want to pay for them.
And he laughed while I thought WHAT THE FUCK? You know that a bridge is going to fall down if it is not eventually repaired and yet you think it is perfectly okay to put it off because you don’t want to pay for it. You must have gone to the same school as Brooks’ student. In fact, interestingly enough, over one-quarter of senators have an undergraduate or graduate degree from an Ivy League institution.
Shortly after I listened to that radio show, I was leaving Gompers Middle School in south central Los Angeles, where I have volunteered for the past two years teaching an after school class. Painted on the wall of one building was this quote from Cesar Chavez,
We cannot seek achievement for ourselves and forget about progress and prosperity for our community…
The remainder of this quote, by the way, is
Our ambitions must be broad enough to include the aspirations and needs of others, for their sakes and for our own.
Clearly, Chavez did not attend an Ivy League school.
What does it take to get into the Ivies these days? Well, it certainly helps to be related to an alumnus. That helps a lot. Attending a private school is strongly correlated with admission. Of course, one needs exceptionally high SAT scores, advanced placement classes help. There have been a number of articles and even a book written by parents (mostly mothers) who give their strategy for putting their child into the Ivy League, many beginning at kindergarten with hours of studying every night and weekend and almost every minute focused on a single goal – that golden ticket of an admission letter.
I’m not arguing that a degree from a subset of schools makes it FAR more likely you will be working on Wall Street or in Washington and far more likely in general that you will make a LOT of money. I am questioning whether that is the whole purpose of life.
People seem to get into the Ivies in largely two ways:
- Being born into privilege. They come from a family of Ivy alumni that gives them an in-road with legacy admissions and who also have the money to send them to top private schools and pay for extras such as tutors and SAT prep classes.
- Being willing to play the game and do as they are told from very early on.
Children who forego playing soccer, football or God forbid some minor Olympic sport for studying will do better academically. Children who put in 8 hours or more in a sport (pretty common at the high school level) will have less time to study. Forget working full-time in high school, or part-time as many students do. The child who studies twelve hours a week beginning in kindergarten will be far ahead by third grade of the child who studies two hours a week. This doesn’t make the first child more intelligent – although he or she will certainly appear so to teachers. It means the second child spent time playing outside, flying a kite in the park (yes, that is what I did with my granddaughter) and maybe laying on the couch watching Strawberry Shortcake videos.
Shouldn’t the students who studied for twelve years get admission over those slackers who watched videos in first grade instead of doing math work sheets? Funny, when I was younger, we had a word for those slackers. We called them “children”.
I do not accept the premise that someone who studied twelve hours a day for a dozen years to be at a given point by age 18 will necessarily be ahead at 25 or 30 or 50. It depends on how you measure ahead.
Where do those students who graduate from the Ivy League schools go? It turns out that a disproportionate number of them go into finance, law school and management consulting. A very small proportion go to education, non-profits, start-ups COMBINED.
It could be argued that those students will go on to run our financial and government sectors. They are disproportionately represented there and those seem to be the two sectors that are causing great problems in the rest of our society. The creative loopholes in the tax code exploited by Apple, the toxic assets created by Wall Street are two examples of exactly what the student from Yale saw as the goal in life, investing in oneself and screw everyone else. As NPR said, isn’t that human nature?
I don’t know. I think I’m human and I was teaching for free at that school with the quote by Chavez on the wall. Cesar Chavez was human.
What an Ivy league education seems to confirm for people is the belief that either a) you are entitled to live a life with privileges not available to others because that is just the way it is or b) do exactly as you are told, don’t question the system and you will be rewarded.
The Spoiled One commented to me recently,
“I’ve thought about going to Harvard but I know some people might think I’m not smart enough because there are two or three people in my class ahead of me.”
I told her,
“You’re plenty smart enough. You don’t work hard enough.”
At this point, I did not, as you might imagine, exhort her to work harder. She has 3.7 or 3.8 GPA at a private college prep school, where she has a scholarship. She plays soccer and volunteers at the food bank to serve meals to homeless people. She recently went to Mexico to help at an orphanage. None of these are things I told her to do. I don’t believe the next three years of her life should be devoted solely to matching a template in some admissions office.
I expect she will go to one of the very many good colleges or universities in this country. It may be one of the Ivies but probably not. At some point, she will choose a path for herself, not follow one I have laid out for her since the day she was born. I have full confidence that she will grow up to be the kind of person who is GOOD for America and not someone who believes that she wasted any second not spent moving herself one step ahead of the next guy.
I trust that she will grow up to be the kind of person who believes in repairing bridges.
I’m not perfect. God am I ever not perfect.
I’ve been working on the Spirit Lake Game beta on and off for the past several weeks, adding, fixing, changing. In most of these cases we knew months ago as we wrote the game that we needed documentation or that we would need to come back and re-design one part or another.
Yet, we made the decision to go ahead last fall and test the game as-is. I cringe a little when I think of all of the work-around and trouble-shooting we required of Dr. Longie, our vastly under-appreciated site coordinator, and the teachers in the pilot classrooms. On the other hand, I feel pretty good about all of the improvements to show them next week when we are in North Dakota.
Even with that work done, daily, I am going in and replacing pages that I knew at the time could be done better. We had framed pages that we replaced with our own code, videos that we replaced with our own videos. I’m making some supplemental games. Marisol and Danny are working the Easter eggs that will pop up in the side quests (thanks to Ronda for suggesting this when she wasn’t busy punching people).
There are SO many reasons for getting something out in the world with all it’s flaw and imperfections rather than waiting until you have a perfect product.
One is apparently contradictory – that is, to put some pressure on to get it done.
You see, if you are working on something that you are going to release, then you have all of the time in the world to make it better. If you have something already in people’s hands, you feel like you damn well better fix whatever that bug is and NOW.
Another one is that with the right people testing it, you will find lots of improvements you hadn’t considered, so you can make many changes in one fell swoop.
Yet another reason is that once people have something concrete in their hands, they know you are serious and not just one of a million other people with an idea. You will get more people who are willing to work with you, work for you, advise you, provide you funding. That’s assuming, of course, that your product doesn’t suck.
Wait, what, didn’t I just say that our alpha version had a ton of glitches, compromises and problems “to be fixed later”. Yes, I did say that, but it was still a good first effort and the students and teachers involved were well aware that they were getting a first effort. We deliberately selected a group who would work with us as collaborators in developing a better product rather than just critics pointing out the flaws.
Similarly, the people who backed us on Kickstarter realized that what they received a few weeks ago was our first beta. There will be an update in a few weeks. We are actually just holding it off so that our new, soon-to-be-hired intern can play the game on several browsers and identify any problems that require immediate attention. So, they got a decent, playable beta version and will get a better version in a few weeks.
By the end of September, we should have that game looking REALLY good along with the first six levels of our next game, as we start to iterate again. We’ll send those same backers another update in January when we roll out the game in several schools.
Through this process we have obtained funding from Kickstarter and USDA, entered into agreements with several schools, met personnel from several other schools interested in working with us AND continually improved the game.
By the time we DO have a nearly-perfect game out there, lots of people will be aware of it and many kids will already be playing it.
The biggest reason to not wait to try something – turning in a paper, releasing a beta test on the market is as a philosopher once said,
The Best is the Enemy of the Good
I had a couple of friends in college who often chastised me for my slacker ways.
One semester, I had a programming class that had a syllabus stating do X number of projects for a C, X+2 for a B, X+4 for an A. Since I was required to keep a B average for my scholarship, I did X+2 projects by the third week and took that time over the remaining 13 weeks to catch up on my sleep. (Hey, it was the mid 1970s and computer programming seemed as likely to be useful in my future career as, say, making integrated circuits.) Those of you who are sniping at my decision probably did not simultaneously attend college, work full time and compete in a varsity sport plus win the national championships in a second sport. I was tired. Also, 17 years old.
Anyway … one of my friends gently scolded me about this and pointed out how he was going to get an A in the class. He wanted me to agree with him that his projects for the course were far superior. Knowing him, I asked if he had turned in his assignments yet. He told me no, he was still improving them. He had too much pride, he said, to turn in work that would earn him less than 100%.
The end of the story …. he ended up taking an incomplete in the class because his assignments never were perfect enough by the end of the semester. He had incomplete grades in several classes and still had three semesters left when I graduated, even though we had started at the same time.
Perfect is good, but getting something done is better.
It must be that time of year because I was asked to speak at two different schools in downtown Los Angeles this week, one elementary school and one middle school. The Perfect Jennifer probably won the coolest teacher award for getting her younger sister, a world champion in mixed martial arts and subject of a made for TV movie this summer to come talk for career day.
However, after the mobs of autograph seekers had departed, there were still plenty of questions for the old mom, just as there were at the elementary school in MacArthur Park (yes the same of disco song and gang fame).
Here are some of my favorite questions and the answers that I gave.
Q. Were you always a math genius?
I was not a particularly good student. I got in trouble a lot for fighting and I wasn’t all THAT interested in school. I think I started being interested in math when I was in the sixth grade just because the math teacher (Sister Marion) was really nice and some of my other teachers were really mean. I mean, really mean, like throwing stuff at me. It’s true, I was an annoying child, but still. Since I liked her, I liked her class, so I studied harder for it and did better.
Q. Is your mother proud of you?
Yes, I believe she is. I’ve gotten a lot of education, started a company that does good work, been a teacher and been able to take care of my children well, so I would say, yes, she is proud of me.
Q. What do you dislike about your job?
I really had to think about this one and for a long time I could not think of anything. Then, The Perfect Jennifer reminded me that sometimes I have to go to North Dakota in the winter. That is the one thing I don’t like about my job, when I have to go somewhere it is really cold because I hate cold weather.
Q. What was your Plan B?
I had to think about that, too, for a while. I finally said that I really like being a statistician and the work that I do and if it doesn’t work out, if the grant that I’m working on now doesn’t get funded, if my game I’m working on now doesn’t sell then I think I will just try again. It’s like my daughter Ronda (who spoke earlier in the morning) said. Someone asked her in an interview once,
“You’ve won every match so far in your career with the arm bar in the first round. What are you going to do if you try the arm bar on someone one day and it doesn’t work?”
“Well, I guess in that case, I’d probably try again.”
(In fact, if you saw her last match, that is exactly what she did.) So, I said, I think my Plan B would be to try again to succeed as a statistician.
Q. What do you like about your job?
Everything. I like traveling. I like working with really smart, nice people which is all I work with any more, because if they are jerks, I just turn down the contract and don’t work with them. I like the fact that every project is something new, sometimes it’s seeing if a program works, some days it’s trying to catch fraud, other days it is teaching a class. I like the fact that I don’t have to get up before 10 o’clock in the morning.
Finally I told them,
If you don’t remember anything else I said or that anyone else said today, remember this, because it took me a long time to figure it out. Don’t EVER believe that other people are smarter than you, that they have some special kind of math brain that they can get it and you can’t, that everyone knows more than you. If they do know more than you it is just because they worked at it longer and harder and if you work long enough and hard enough you will get to the same place. Don’t believe you need to be a certain race or age or look a certain way to start a technology company and be successful. It just is not true. I used to think that way, that people who are really good at math were not people like me, certainly none of the math professors I had in college or people I saw on television talking about starting companies looked like me. None of that matters. Now I write the sort of things that I could not imagine even understanding when I was young and I toss it off like it’s nothing and it IS nothing because I’ve been doing it for twenty years. Math, martial arts, programming – anything – you just bang away at and you get it eventually. Why do you think they call it hacking?
Last week I wrote a bit about how to get an exploratory factor analysis using Mplus. The question now, is what does that output MEAN ?
First, you just get some information on the programming statements or defaults that produced your output:
INPUT READING TERMINATED NORMALLY
Exploratory Factor Analysis ;
SUMMARY OF ANALYSIS
Number of groups 1
Number of observations 730
Number of dependent variables 6
Number of independent variables 0
Number of continuous latent variables 0
Observed dependent variables
Q1F1 Q2F1 Q3F1 Q1F2 Q2F2 Q3F2
Row standardization CORRELATION
Type of rotation OBLIQUE
This tells us we our analyzing all of the data as one group, and not, for example, separate analyses for males and females. We have 730 records, six variables, all of which are continuous and listed above. The maximum likelihood method (ML) of estimation is used and the default rotation, GEOMIN, which is an oblique method, that is it allows the factors to be correlated.
Here we have a list of our eigenvalues
RESULTS FOR EXPLORATORY FACTOR ANALYSIS
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
1 ……… 2 ……… 3 4 5
________ ________ _____ ________ ________
1.866 1.262 0.866 0.750 0.716
EIGENVALUES FOR SAMPLE CORRELATION MATRIX
In this case, you could go ahead with the eigenvalue greater than one rule, but let’s take a look at a couple of other statistics. First, we have the results from the one factor solution. Here we have the chi-square testing the goodness of fit of the model
Chi-Square Test of Model Fit
Degrees of Freedom 9
We want this test to be non-significant because our null hypothesis is there is no difference between the observed data and our hypothesized one-factor model. This null is soundly rejected.
Let’s take a look at the Chi-square for our two-factor solution
Chi-Square Test of Model Fit
Degrees of Freedom 4
You can clearly see that the chi-square is much smaller and non-significant.
Let’s take a look at two other tests. The Root Mean Square Error of Approximation (RMSEA) for the one-factor solution is .115, as shown below. We would like to see an RMSEA less than .05 which is clearly not the case here.
RMSEA (Root Mean Square Error Of Approximation)
90 Percent C.I. 0.095 0.137
Probability RMSEA <= .05 0.000
For the two factor solution, our RMSEA rounds to zero, as shown below
RMSEA (Root Mean Square Error Of Approximation)
90 Percent C.I. 0.000 0.049
Probability RMSEA <= .05 0.954
Clearly, we are liking the two-factor solution here, yes? The eigenvalue > 1 rule (which should not be TOO emphasized) points there, as does the model fit chi-square and the RMSEA.
In their course on factor analysis, Muthen & Muthen give this very nice example of a table comparing different factor solutions using the data
They also like the scree plot, which I do, too. I also agree with them that one should never blindly follow some rule but rather have some theory or expectation about how the factors should fall out. I also agree with them in looking at multiple indicators, for example, scree plot, chi-square, RMSEA and eigen-values.
Many people have commented how ironic it is that I’m writing computer games these days because I’m one of the least playful people you’ll meet.
I have a confession to make, although confession is perhaps the wrong word because I don’t feel the least bit bad about it.
Playing with small children bores me.
Don’t get me wrong – I love my children and grandchildren and I would do anything for them. I taught my children to read, took them to soccer/ judo/ track/ swim practice , to piano/ bassoon / guitar/ drum lessons and ballet / tap/ hip-hop classes. I worked thousands of hours of overtime to pay for camps in Europe, in marine biology, private universities.
And yes, I went to the park, played with my little ponies, pushed children on swings, threw them up in the air (and caught them – any problems they have are NOT because they were dropped on their heads at a young age no matter how much their behavior during adolescence might lead you to believe otherwise). I read The Perfect Jennifer her favorite book – Where the Wild Things Are – so many times that I still have it memorized years after she finished graduate school.
AND YET …. when I hear those women rave about sitting down with their children and eating carrot sticks while they played with my little ponies together were the most fulfilling moments of their lives, I think to myself,
What? Are you fucking kidding me?
And apologies to the nice man at SAS Global Forum who reminded me that some people read my blog at work and asked me if I could not swear quite so much. I did post four days in a row on factor analysis and no swearing was involved, so I made a good faith effort, I really did.
Seriously, though, that’s what fulfills you? My little ponies?
Because as I was listening to my granddaughter talk about my little ponies what was going through my head was how I could use a statistical test for the difference in sample proportions to prove that a set of data I was asked to analyze was fraudulent. I’ll probably post about that next week. I was also intrigued by the very simple way the Muthuens had demonstrated comparison of competing factor solutions by using a table showing the chi-square, RMSEA and presence/ absence of Heywood cases.
When my four-year-old granddaughter told me she wanted to be a princess when she grew up I told her,
Princesses suck and I hate princesses. They’re useless and they don’t DO anything.
To which my darling daughter number one responded that “we” don’t say “hate” and “we” don’t say “suck” and I believe she muttered under her breath something about it being a wonder that she turned out normal with a mother like me. Obviously, this is a new meaning of the word “we” that doesn’t include the other person.
I am certain that I muttered under my breath, “Well, it’s true. They DON’T do anything useful.”
As penance I was forced to go to Disneyland and visit the Pavilion of Princesses. My granddaughter ADORED it. I was bored out of my mind by the princesses but the radiant look on her face DID make it worth taking a day away from work and paying Disneyland the equivalent of the median annual income in many countries for seven of us to eat churros and buy random pink crap bearing the stamp of useless women a.k.a. princesses.
The truth is, as much as I truly loved my children – and I had three under age five while working on my PhD – at the end of each day, when they were all asleep, I sighed deeply, sat down and read books on multivariate statistics and matrix algebra and was satisfied with life. I did NOT wish they would wake up so we could dress up like princesses.
There you have yet another of the 55 things I have learned in (almost) 55 years – you can be bored to death by Curious George, Strawberry Shortcake and every other thing designed to appeal to people with the mind of a three-year-old and still be a good mother.
It reminds me of a story I heard about someone who had a son who was crazy about baseball. The father bought season tickets, attended every home game and when the team made the World Series he flew to whatever city it was being held in to attend the games. When someone said to him,
I never knew you loved baseball so much.
I don’t. I think baseball is the most boring game ever invented. But I love MY SON that much.
Previously, I discussed how to do a confirmatory factor analysis with Mplus. What if you aren’t sure what variables should load on what factor? Then you are doing an exploratory factor analysis. Really, you should probably do the exploratory factor analysis first unless you have some very large body of research behind you saying that there should be X number of factors and these exact variables should load on them. If you’re analyzing the Weschler Intelligence Scale, you probably could skip the exploratory step. For everyone else …. here is how you do an exploratory factor analysis with Mplus.
TITLE : Exploratory Factor Analysis ;
Data: FILE IS ‘values.dat’ ;
VARIABLE: NAMES ARE q1f1 q2f1 q3f1 q1f2 q2f2 q3f2 ;
ANALYSIS: TYPE = EFA 1 3 ;
ESTIMATOR = ML ;
When no rotation is specified using the ROTATION option of the ANALYSIS command, the default oblique GEOMIN rotation is used.
The fourth statement is new. Like the other statements, you need to follow the ANALYSIS key word with a colon and end each statement in the command (or if you are familiar with SAS, think of it as a procedure) with a semi-colon.
TYPE = EFA 1 3 ;
Requests an exploratory factor analysis with a 1 factor solution, 2-factor solution and 3-factor solution. Of course, depending upon your own study, you can request whatever solutions you want. This is really useful because often in an exploratory study you aren’t quite sure of the number of factors. Maybe it is two or maybe three will work better. Mplus gives you a really simple way to request multiple solutions and compare them. I’ll talk more about that in the next post.
ESTIMATOR = ML ;
requests maximum likelihood estimation.
If you are interested in factor analysis at all, there is a really good video on the Mplus site. Far more of it discusses exploratory and confirmatory factor analysis – methods, goodness of fit tests, equations, interpretation of factor matrix – than Mplus, which as you can see, is pretty easy, so even if you are using some other software the video is definitely worth checking out.
Being able to find SPSS in the start menu does not qualify you to run a multi-nomial logistic regression.
This is the kind of comment statisticians find funny that leaves other people scratching their heads. The point is that it’s not that difficult to get output for some fairly complex statistical procedures.
Let’s start with the confirmatory factor analysis I mentioned in my last post. Once you get past the standard stuff that tells you that your model terminated successfully, the number of variables and factors, you see this:
Chi-Square Test of Model Fit
Degrees of Freedom 8
The null hypothesis is that there is no difference between the patterns observed in these data and the model specified. So, unlike many cases where you are hoping to reject the null hypothesis, in this case I certainly do NOT want to reject the hypothesis that this is a good fit. As you can see from my chi-square value above, this model is acceptable.
Another measure of goodness of fit is the root mean square error of approximation (RMSEA).
RMSEA (Root Mean Square Error Of Approximation)
90 Percent C.I. 0.000 0.046
Probability RMSEA <= .05 0.973
An acceptable model should have an RMSEA less than .05. You can see above that the estimate for RMSEA is .011, the 90 percent confidence interval is 0 – .046 and the probability that the population RMSEA is less than .05 is 97.3%. Again, consistent with our chi-square, the model appears to fit.
…………………Estimate S.E. Est./S.E. P-Value
Q1F1 1.000 0.000 999.000 999.000
Q2F1 1.828 0.267 6.833 0.000
Q3F1 1.697 0.235 7.231 0.000
Q1F2 1.000 0.000 999.000 999.000
Q2F2 1.438 0.291 4.943 0.000
Q3F2 1.085 0.191 5.687 0.000
Here are the unstandardized estimates. By default the first variable for each factor is constrained to a value of 1, so, of course, there is no real standard error, probability or standard error of estimate. It isn’t really an estimate, that was set. Let’s look at the other two. Since they are unstandardized the more useful measure for us is the estimate divided by the standard error of the estimate, for example 1.828/ .267 . This is done for us in the column under Est. / S.E. and in that case comes out to 6.833. You interpret these values in the same way as any z-score, with 1.96 as the critical value, and you can see in the last column that all of my variables loaded on the factor hypothesized with a p-value much less than .05.
The next thing I look at is the residual variances. At this point my only concern is that I *not* have a residual variance that is negative. It makes no sense that you would have a negative variance because (among other reasons) variance is a sum of squares and squares cannot be negative. Also, in this case, the commonality is greater than 1, meaning you have explained over 100% of the variance in this variable by its relation to the latent construct. This also makes no sense. These are referred to as Heywood cases and explained beautifully here (even though the linked documentation is from SAS it applies to any confirmatory factor analysis).
The final thing I want to look at, for right now, anyway, is the R-squared
Variable Estimate S.E. Est./S.E. P-Value
Q1F1 0.142 0.032 4.473 0.000
Q2F1 0.475 0.065 7.256 0.000
Q3F1 0.438 0.061 7.123 0.000
Q1F2 0.174 0.045 3.883 0.000
Q2F2 0.376 0.078 4.827 0.000
Q3F2 0.179 0.044 4.057 0.000
You can see that the r-square is pretty decent overall. These are interpreted just like any other R-square values. I didn’t show the standardized factor loadings here but just take my word for it that the R-squared values are the standardized loadings squared. So this is the variance in q1f1, for example, explained by factor 1.
I started this whole thing working with Mplus to do a factor analysis and overall, I’d have to call it a pretty painless experience.
Someone had a question about factor analysis with Mplus and even though it is not a piece of software I work with normally, we aim to please at The Julia Group, so I downloaded the demo version and away I went.
It truly was, as my granddaughter says, easy-peasy lemon squeezie.
You might not think so, because the first thing you are confronted with is pretty much a blank window like this
1. Create a .dat file from the original file. The file was in a SAS format and I did not have SAS on the laptop I was working on (I’m in Cambridge, MA at the moment). What I did was
- Open the file in SPSS by, from the FILE menu selecting READ TEXT DATA and then selecting SAS as the format
- Ran this SPSS command from the syntax window to output a tab-delimited file with no header, which was the type of input Mplus would expect.
2. Type in this program to do a two-factor solution with the first three variables loading on the first factor and the next three loading on the second factor.
TITLE : Confirmatory Factor Analysis ;
DATA: FILE IS ‘/Users/annmaria/Documents/mplustest/values.dat’ ;
VARIABLE: NAMES ARE q1f1 q2f1 q3f1 q1f2 q2f2 q3f2 ;
MODEL: f1 BY q1f1 q2f1 q3f1 ;
f2 BY q1f2 q2f2 q3f2 ;
OUTPUT: standardized ;
3. Click the RUN button.
That is really all there was to it.
Okay, well that is easy if you knew what to type so let me explain a few things. If you know SAS or SPSS this will be easy.
Each of those things that I put in all capitals is a command in Mplus, analogous to a DATA or PROC step in SAS and a command in SPSS. They don’t need to be in all caps, I just did that for ease for the reader. They DO need to be followed by a colon and then end the statement in a semi-colon.
Title – pretty obvious, gives your output a title.
DATA: FILE IS — gives the path to locate your data.If your file is in the same directory as your program, you don’t need a fully qualified path and can just call it ‘values.dat’
VARIABLE: NAMES ARE
Give the names of your variables. You can specify a format but if you do not Mplus assumes they are in free format, which is the same as what SAS refers to as list format. You might want to note that if you are using the demo version you can only have a maximum of 6 independent and 2 dependent variables.
MODEL: This is my model (duh) and I am modeling two factors. The first factor I creatively named f1 and it is represented BY (notice the BY in the command) variables also creatively named q1f1 q2f1 and q3f1.
Similarly, I have a second factor named f2 ;
I added an OUTPUT statement with a standardized option because I wanted (surprise) standardized estimates. That statement is not required but as you’ll see in my next post on interpreting factor analysis data, you do want it.
I am intrigued by Mplus. It sort of assumes you have close to perfectly cleaned up data because I wouldn’t want to be doing a lot of data management with it, but for doing some relatively complex models – factor analysis, path analysis, structural equation modeling – it looks pretty cool.
Here are four more of Dr. De Mars 55 things I have learned in (almost) 55 years, and that is that there are four thing students should have learned in school but often didn’t.
1. Say what you mean. I don’t know who those teachers are who reinforce students for using longer words, longer sentences and writing more pages but I hope someone finds them and beats them senseless with The Elements of Style , which nearly a century after it was first published I still think is one of the best books on writing out there. When you write,
In the experiment under discussion we utilized two conditions in the manner such that one group of the subjects referred to in the preceding paragraph received no treatment, that is, they were what is referenced as the control group. The other group, that is the second group, which was the group receiving our treatment described in the section under procedures which follows is hereafter referred to as the treatment group. A treatment group is defined by Academic-Guy (2012) as …
Subjects were randomly assigned to either a treatment or control group.
You may think the first example makes you sound intelligent and well-educated but it doesn’t. It makes you sound like you learned English by watching the Power Puff Girls and imitating Mojo Jojo. People – clients, your boss – are busy, and grant applications have page limits.
2. Don’t be a pain in the ass. I wrote a post about this, Why the cool kids won’t hang out with you. In brief, no matter how smart you are, if you constantly run down your co-workers, flaunt the policies of your organization and are rude to your boss, at some point they will replace you with an equally smart person who is less of a pain. This may sound hypocritical because if you have been reading this blog for long you are well aware that I swear, don’t do mornings and, if I have to wear a suit, I charge extra. However, I work with clients that are cool with that.
Really points 1 & 2 generally reveal a person trying to prove that he or she is smarter than the other people in the room. That usually reflects an underlying insecurity. I have met some absolutely brilliant scientists and businessmen/women. None felt the need to try to impress me. I was already impressed when I met them, and I’m sure that was the reaction they got from almost everyone.
3. Mean what you say. If you say you will be in the office at 8 a.m., be in the office at 8. I tell clients I will be in by 9:30 or 10 if necessary because I know there is no way on God’s earth I am dragging myself out of bed at 7 a.m. It’s not happening. On the other hand, they know that if I say I will be in by 10, I will. If you say you can write programs in Perl or are experienced creating multi-media PowerPoint presentations, then when I ask you to do that, you should be able to do it. [I don’t really need anyone to do either so if you are applying for our summer intern position, you don’t need to mention these. It was just an example.]
4. Learn to code. It doesn’t matter what language. It’s absolute bullshit that once you know one programming language you know them all, but it is certainly true that once you have the idea of loops, arrays, properties, methods, classes, extend, functions and a few dozen other key concepts, it will be much easier for you to pick up a second, third or fourth programming language. The Perfect Jennifer is an amazingly great history teacher and she is in one of the minority of fields where you can not do any programming and have a decent, stable job. Did I mention she is amazingly great, and works an enormous amount of extra hours? However, if you are planning on going into consulting, management or a large number of other fields, knowing how to code will help you immensely. Even our Chief Marketing Officer, who only focuses on marketing, has done a little coding and has some idea of the constraints of developing a new product. I’m so convinced of the personal and professional value of learning at least a little bit of programming that I have gone back to requiring it in my statistics courses. Often students don’t learn to code because they underestimate themselves. They believe programming is done by people who are smarter, more focused or in some way better than them. That’s simply not true and learning to code will give them both more skills and more confidence.
So, those are four more things I have learned in (almost) 55 years and that I think any student graduating should learn as well.