Test of confidence intervals? In one of my assignments I have to "test" if the confidence intervals for a set of parameters in a mixed effect model is accurate. I'm asked to simulate from fittet parameters and there after refit them using the same model many times, and lastly take 2.5% and 97.5% quantiles of them and compare with the original CIs. My question is, how does this procedure in anyway measure how accurate my original confidence intervals are?

odcinaknr 2022-10-02 Answered
Test of confidence intervals?
In one of my assignments I have to "test" if the confidence intervals for a set of parameters in a mixed effect model is accurate. I'm asked to simulate from fittet parameters and there after refit them using the same model many times, and lastly take 2.5% and 97.5% quantiles of them and compare with the original CIs. My question is, how does this procedure in anyway measure how accurate my original confidence intervals are?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Danielle Gilbert
Answered 2022-10-03 Author has 5 answers
Step 1
Each time you simulate data from fitted parameters you find another estimate of the parameter. If the original 95% CI is valid, about 95% of these new estimates ought to lie in the original CI.
You must be studying, or about to study, parametric bootstrapping. There are so many different formulations of this idea that I hesitate to get into a theoretical discussion, without knowing the particulars of your course and text, for fear of causing additional confusion.
Take a very simple case. I have a sample of n = 36 observations from N o r m ( μ , σ = 10 ) .. Suppose X ¯ = 105.9 ,, so that a 95% z-interval for μ is 106.9 ± 1.96 ( 10 / 6 ) or (103.6,110.2)Now I take a large number, say B = 100000 ,, of samples of size 36 from Norm(106.9,10) and use R to carry out the procedure you describe.
B = 10 5 ; m u . e s t = 106.9 ; s g = 10 ; n = 36 R D T A = m a t r i x ( r n o r m ( B n , m u . e s t , s g ) , n r o w = B ) x . b a r = r o w M e a n s ( R D T A ) each row of B x n matrix is a sample quantile ( x . b a r , c ( .025 , .975 ) ) 2.5 %   97.5 % 103.6111   110.1773
Step 2
The result is not far from the original CI (103.6,110,2). In this trivial case, the agreement is not surprising because we are just re-establishing by simulation that X ¯ N o r m ( μ , σ / n ) .
In more complex cases, modifications must be made in the procedure, especially when dealing with distributions and estimators that have heavily skewed distributions.
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2020-12-27

Consider the next 1000 98% Cis for mu that a statistical consultant will obtain for various clients. Suppose the data sets on which the intervals are based are selected independently of one another. How many of these 1000 intervals do you expect to capture the corresponding value of μ? 
What is the probability that between 970 and 990 of these intervals conta the corresponding value of Y =the number among the 1000 intervals that contain What kind of random variable is Y) (Use the normal approximation to the binomial distribution)

asked 2021-08-12

Anna flipped a coin to choose either her right hand or her left hand, and also she asked the therapists to identify the named hand by placing their hand just under Anna's hand without seeing it and without touching it. Among 358 trials, the touch therapists were correct 172 times. Complete parts​ (a) through​ (d).
a) Given that Anna used a coin toss to elect either her right hand or her left hand, what proportion of correct responses would be anticipated if the touch therapists made arbitrary suppositions?( Type an integer or a numeric. Do not round.)
b) Using Anna's sample results, what's the stylish point estimate of the therapists' success rate?( Round to three decimal places as demanded.)
c) Using Anna's sample results, construct a 90% confidence interval estimate of the proportion of correct responses made by touch therapists.
Round to three decimal places as demanded-?<p<?

asked 2021-08-04

The average annual mileage of a car is 23,500 kilometers, with a standard deviation of 3900 kilometers, according to a sample of 100 Virginians who own cars.
Assume that the measurement distribution is roughly normal.
a) Create a 99 percent confidence interval for the typical Virginian vehicle's annual mileage in kilometers.
b) If we assume that Virginians drive an average of 23,500 kilometers per year, what can we say with 99 percent certainty about the potential extent of our error?

asked 2021-01-10

The average zinc concentration recovered from a sample of measurements taken in 36 different locations in a river is found to be 2.6 grams per liter. Find the 95% confidence intervals for the mean zinc concentration in the river. Assume that the population standard deviation is 0.3 gram per liter. (Z0.025=1.96,Z0.005=2.575)

asked 2021-12-17
An article regarding interracial dating and marriage recently appeared in a newspaper. Of the 1713 randomly selected adults, 301 identified themselves as Latinos, 325 identified themselves as blacks, 255 identified themselves as Asians, and 778 identified themselves as whites. Among Asians, 79% would welcome a white person into their families, 71% would welcome a Latino, and 66% would welcome a black person.
If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
Construct the 95% confidence intervals for the three Asian responses. (Round your answers to four decimal places.)
Construct the 95% confidence intervals for the three Asian responses. (Round your answers to four decimal places.)
a) Welcome a white peron.
b) welcome a black person.
c) welcome a latino
asked 2022-03-22
Let X1,,Xn random sample of U[θ12;θ+12].Consider [X(1); X(n)] a confidence interval for θ. Find their confidence level and show that result is valid for any distribution symmetric around θ
asked 2021-03-06
Based on a sample of 80 recent Masters graduates (40 male and 40 female), the following information was made available regarding their annual salaries. The standard deviation of salaries for the male graduates was $40,000 and that for the female graduates was $25,000.
a) For the male graduates, what is the probability of obtaining a sample mean salary within $10,000 of the population mean?
b) Consider the same question in (a) but for the female graduates. In which case, males or females, do we have a higher probability of obtaining a sample estimate within $10,000 of the population mean? Why?
c) Suppose that the sample mean salary of females is $125,000. Develop a 95% confidence interval estimate for the mean salary of all female graduates

New questions